Well, first of all, welcome to the club. Most of us here probably have one or more copies of the TNG:TM, and other TMs and encyclopedias, etc. This is the place to be if you love having that stuff, and love discussing it.
Now, as for the Galaxy, you're on the right track. The Galaxy most definitely is not a 'failed starship', and she is most definitely one of the greatest and most potent Capital Ships Starfleet has produced, and she has a long service life ahead of her, much like the Excelsior. Now, like the Excelsior, she won't always fill the role of premier Capital Ship - as she ages she'll slowly move down in role, eventually dropping low enough, relative to modern ships, to the point where she will probably only compare to a modern Light Cruiser at the end of her lifespawn. But that is a long time away, and Starfleet tends to produce a new generation of premier capital ship every 20-30 years or so. The average lifespan of any given capital ship, from TOS to TNG, has been about 20-30 years. So we should be expecting to see a replacement for the Galaxy class launched sometime in the mid-2380s to mid-2390s. The Sovereign is far too soon to be a replacement for the Galaxy class, especially given the remarkable performance we generally see from the Galaxy.
I can understand your position on not wanting to think of Federation ships in terms of warship designations, but those ratings are still a part of each starship's role and mission. They are not the entirety of their role, but that is still their role, nonetheless. We shouldn't focus on those parts of a Federation starship's role exclusively, but we shouldn't ignore them, either. Starfleet ships are intended to be the defense force of the Federation, after all, and they have generally shown themselves to be very capable combat ships when called to the task. They're just much more than pure combat ships. As such, I tend to use the military rating designations, partly because it designates a major role for the ship, and also partly because it allows for a fairly ordered rating of ship roles even beyond military roles and duties. For the sake of inclusiveness and organization, I'll use that rating system here, alongside the non-combat roles and mission parameters.
Now, we know that the Galaxy class Enterprise-D was the flagship of the 7th Fleet and the flagship of the Federation, but we have no indication that either title was transferred to the Enterprise-E. It's entirely possible, and I wouldn't be surprised if both titles were transferred to the new Enterprise, but we have no actual confirmation of such. Just for the record.
Undoubtedly, the Sovereign's design was influenced by many different things over the course of its development. The close of the Federation-Cardassian War, the First Borg Incursion, subsequent encounters with the Borg, and several advances in warp design, phaser design, torpedo technology, and more. But I do not think that her base mission and intended purpose were changed. Per Rick Sternbach from a long-ago post on the TrekBBS forums, the Sovereign was designed to replace the Excelsior as the premier workhorse cruiser of the fleet.
Now, first, to understand this we must take a look at the Excelsior and her service period, and the ship design practices of the Federation over the course of the Excelsior's lifespan. When the Excelsior launched in 2285, she was Starfleet's premier capital ship. A gargantuan starship, she featured the latest and greatest technology, in all fields. She was also a powerful Battleship in combat, designed not only to carry out Starfleet's scientific, diplomatic, and exploratory functions as a deep-space explorer, but also to defend the Federation as her premier Capital Ship, her premier Battleship, at the height of the Federation-Klingon Cold War. She was as much a potent warship as she was science vessel, and sported an impressive array of armaments, including an astounding twenty-eight ball-turret phaser cannons and a whopping EIGHT photon torpedo launchers, four fore and four aft, with two of the fore launchers being mounted on giant turrets that could swing nearly 90 degrees to either side, giving her the ability to fire torpedoes sideways. She was an impressive starship, ushering in a new warp technology (the 'transwarp drive' of the Excelsior likely became known as just 'warp drive' after its common implementation, much like the 'time warp drive' that replaced the original 'warp drive' when the Constitution class was new). She was made even more impressive when the Type-B variant was launched with the Enterprise-B in 2293, featuring an expanded stardrive section, additional impulse engines, enhanced warp nacelles, four additional phaser turrets, and a plethora of other new advances, and this served to help extend her service life. But by the 2320s, the Excelsior was showing her age. New technologies developed around the turn of the century made many of the state-of-the-art technologies on the Excelsior less grand, and in 2323 she was replaced by the Ambassador class, an absolute monster of the ship at the time, twice as large relative to the other ships of the day as the Galaxy class was to the ships of her day.
But the Excelsior was far from obsolescent. She could no longer perform as a capital ship, but Starfleet had built a lot of them, and they were still very potent cruisers, and very capable starships. For the first half of the 24th Century, Starfleet only produced a bare handful of new cruisers, opting instead to mass-produce the Excelsior class. The Excelsior became the workhorse of the fleet, along with the Miranda class, which had a similar story in the role of Light Cruiser and Destroyer. The Excelsior excelled in this role, and she became the face of Starfleet.
But by the 2350s, the Excelsior was really showing her age. She could no longer properly fill the role of Heavy Cruiser, not in combat roles, and even in non-combat roles, while still a capable workhorse, the limitations of her age were showing. The Federation was also undergoing one of its bloodiest periods in history, second only to the Dominion War. The 20-year-long war with the Cardassian Union was in full swing in the 2350s, the Federation also engaged in war with the Tzenkethi, the Talarians, and probably also the Tholians (at the very least, there was an extended border conflict and cold war, which saw the destruction of at least one Federation starbase). So the Federation launched the Springfield, Cheyenne, Challenger, and New Orleans class cruisers, all designed to replace the Excelsior, and in some respects the Miranda (which was showing her age even more). The Excelsior had taken up the role of doing almost everything in the fleet, and to replace her, Starfleet had to design several new classes to fill specific roles. The Springfield was an all-around, jack-of-all-trades starship - capable of most tasks, but not particularly great at any one task. By size she would rate a Heavy Cruiser, though just barely, and is more a big, general-purpose cruiser. The Cheyenne is a relatively small Light Cruiser, slim, but very fast, with four nacelles. One of the fastest ships in the fleet, she's a long-distance runner. The Challenger is another Heavy Cruiser, but much of her size comes from her over-sized nacelles. Another fast ship, the Challenger's biggest feature are her massive phaser arrays - her two big saucer arrays (the only phasers on the ship) are the largest phaser arrays mounted on any ship smaller than a Nebula. She's a big-gun phaser boat that can be moved around fast. Outside of combat operations, she probably fills the role of a general-purpose cruiser, much like the Springfield, but less capable for her size. Then there is the New Orleans, one of my favorites. Coming in at just under 1.1 million cubic meters in volume, the New Orleans is one of the largest Heavy Cruisers Starfleet has produced, and when she launched she was THE largest Cruiser Starfleet had produced to date. She was also a very multi-role starship, especially with the three swappable pods she could be equipped with, giving her the ability to specialize in a wide array of mission parameters on relatively short notice.
Then the 2360s came. With the launch of the Nebula and Galaxy class starships, Capital Ships and Battleships both, and the introduction of the newer cruisers, the Cardassian Wars came to a close (it was a major war, but never more than a border conflict for the Federation, and once the new Starfleet cruisers and capital ships hit the field, the Cardassians crashed their economy for a second time just trying to keep up). Newer technologies and bigger ships were coming off the line, however, and Starfleet's replacement program for the Excelsior and the Miranda was not over. The 2360s saw the launch of the new Akira class Heavy Cruiser - dwarfing even the New Orleans at 1.6 million cubic meters in volume. A powerful cruiser with a swappable sail pod, the Akira was a powerful and broadly capable Heavy Cruiser that could go from a devastating torpedo boat to a specialized science ship in short order (TNG-era Starfleet likes swappable pods, and can you blame them?). The Intrepid was introduced in the late 2360s, taking up the role of a sprinting Light Cruiser. She could sprint faster than the Cheyenne, but was limited in how long she could maintain that speed by her small nacelles, making her a potent courier and short-range explorer and patrol ship. The Saber showed up in the late 2360s as well, taking over from the Miranda along with the 2340s-era Freedom class. The 2370s came around and the Steamrunner launched, providing a potent, durable, bulldog of a Light Cruiser torpedo platform. Several other cruisers were launched in the 2350s, '60s and '70s, though most appear to have been fairly specialized designs, built for very specific roles or tasks and not produced on a very large scale (see the USS Yeager, among others).
All of these ships together took over the plethora of roles that the Excelsior had taken on during the first half of the 24th century, but none of them actually replaced the Excelsior as the premier, workhorse cruiser, the face of the Federation. It was to that end that the Sovereign was designed. Not a Battleship, not a Battlecruiser, not a Dreadnought, the Sovereign is first and foremost a workhorse cruiser. She's big, a monster of a Heavy Cruiser coming in at ~2,000,000 cubic meters in volume, dwarfing even the big Heavy Cruisers like the New Orleans and the Akira, though she is not quite large enough to be considered a Capital Ship, not by modern standards. She's sleek, and fast - clocking in at Warp 9.985 according to back-stage info released with the TNG blu-ray set, which would make her the second-fastest ship in the fleet, out-stripping even the Intrepid in a full sprint, and second only to the four-nacelled Prometheus. The Sovereign featured a plethora of new advancements, and a potent armament, though she doesn't sport enough firepower to fall into the category of a Capital Ship. The Sovereign is the new premier cruiser of the fleet, however, featuring state-of-the-art technology, equipment, and a full suite of sensors and science labs, as well as luxurious appointments and diplomatic suites comparable to even a Galaxy class. She can't go toe-to-toe with the capital ships of other powers, especially their newer capital ships, but she can still hold her own quite well, if it comes to that. The Sovereign is Starfleet's greatest Heavy Cruiser ever built, she's the new 'face of the fleet', a potent and powerful and vastly capable starship, that in many ways is a far closer representation of the original Star Trek ship, the Constitution, than the Galaxy class could ever be (she's a powerful, capable cruiser, but she's a workhorse, not a Capital Ship, not a Battleship).
And yes, I'm a Sovereign fanboy. } : = 8 )
