He's pulling it from the TNG:TM, which is a good 'semi-canon' source when used in support of canon materials, but it has errors. For example: We know that Federation phaser rifles are capable of sustained megawatt-range continuous beam discharges for extended periods (a minute or more), because Geordi and Data tested a Romulan replica of a Federation phaser rifle in TNG "The Mind's Eye" by test-firing it with a continuous beam with an output of a little over 1 MW for around a minute. The weapon was a Romulan-built replica, but it was a near-perfect copy, with only a minor emitter crystal efficiency difference, and the only give-away coming from the telltale traces left by the power charging method. The performance was otherwise within specs for a standard Federation Type-III phaser rifle.
Now, as for the actual performance of the Type-III rifle, that was probably the equivalent of taking an M-16, attaching an over-sized box magazine, putting it on a mount and firing it continuously on full-auto. You're not going to do that in combat, because it wastes 'ammo', and just causes all sorts of unnecessary, and potentially dangerous collateral damage. It's also hard on the equipment.
In actual, real-world combat, not even support gunners with Squad Automatic Weapons or Light Machine Guns spray and pray. Trained support gunners still fire in bursts in most situations. Support gunners in Trek would have a little more leeway because they won't run out of ammo as quickly, but the concern is still there, as well as wear on the equipment. Now, of course, there are times when you do just want to obliterate an area, but an air burst from a photon grenade would be a more effective weapon choice than a phaser.
It's also worth noting that Trek phasers can be set to wide-beam for area-effect. This will have limited utility, particularly over large areas and/or extended ranges, because of the inverse squared law, but Tuvok demonstrated how it can make a very effective room sweeper in that one episode where he stunned the entire bridge with a Type-II phaser (can't remember the name off-hand).
When it comes to starship combat, you have all the concerns of energy usage and equipment wear, but you also have concerns about time-on-target, and others. Spray-and-pray with phaser beams in space is hopelessly inefficient because of the distances involved. Short, precise hits are far more efficient, and also reduce the chance of friendly fire incidents (also a factor for ground-force phasers). There is also the concern of Joules vs Watts. A low-powered beam can deliver the same amount of energy (Joules) over an extended period of time, but it won't be as effective as a short, high-energy burst delivering the same amount of energy over a short period of time, because the energy-per-second (Watts) will be lower. It's the difference between standing in the sun collecting rays for 15 minutes, and having that same energy delivered to you in 15 milliseconds. Spread over 15 minutes time, you'll get a tan, or maybe a light sunburn, but delivered in 15 miliseconds you will be severely burned. The same applies to phasers.
The way Trek shields work also makes high-wattage blasts much more effective against shields because, per the TNG:TM (which matches what we see on-screen), shields maintain a relatively low-level continuous protective field around the ship, a field strength that they can sustain for what is effectively an indefinite time (not factoring in extended wear on the equipment, etc.). When weapons fire strikes the shield, the generators then spike their output several orders of magnitude above their sustained output, while also concentrating field strength around the point of impact. This draws energy from the reserves, and also causes the generators to overheat; the spike can only be sustained for very brief periods (<1 second at maximum spiked output, with longer durations for lower output spikes) before the generators overheat themselves and have to reduce power or shut down to avoid melting themselves. This leaves a brief but notable window when the weapons first hit where only a relatively small percentage of the total energy blast is going to be deflected by the sustainable shield strength, allowing a very brief instant of 'bleed-through' damage before the shields spike up. A short, high-wattage blast will deliver much more energy to the target in that brief window, causing more bleed-through damage, than a lower-wattage sustained blast. The high-wattage blast will also cause more wear on the shield generators, forcing them to spike higher and inundate themselves with more waste heat, making them more prone to overloading.
Also, the nature of how phaser arrays work also explains the utility of a short beam vs a sustained beam in combat. As the glowy charge moves across the length of the array, we're actually seeing each emitter individually discharge into a collected energy blast that is directed at the target at the final emission point, allowing for the entire array to contribute to a much more powerful blast than a single array segment could generate on its own (the limitation appears to be not with the emitter crystals that we see on top, that refine and direct the phaser energy, but the components underneath each crystal that actually convert the raw EPS plasma energy into phaser energy). This collected blast would be discharged in the same amount of time that each segment discharges into the collected pool (or the amount of time the glow effect takes to pass over an individual emitter segment), which would be a pretty short span of time, usually significantly less than a second. A beam sustained afterward, which usually only has a few emitters around the emission point glowing and so only a few emitters actually contributing to the beam, would simply not be able to match the power of the full array discharge, making sustained beams far less effective in combat, and explaining why we almost never see sustained beams in combat and usually only see them used for relatively low-power utility activities (drilling precise holes in planets or asteroids, etc.). The only exception to this is in TNG "Best of Both Worlds" when the E-D was sustaining a beam that was cycling through frequencies trying to disrupt a Borg holding beam, and even then, multiple rapid pulses can be seen passing across the array while the beam is still discharging, meaning that the sustained beam was actually pulsing between high and low wattage during the event. There is also a partial exception to this in DS9 "What You Leave Behind" when one of the Galaxies in the background can be seen to fire its main dorsal array with a large glow effect that travels across the array to the emission point, and is then sustained very briefly after the beam is discharged, instead of passing into the emission point as we see with all other phaser operations.
