The story works on top of free play mode, if you choose to leave the storyline you can go exploring (although that may have consequences depending on where you are with the story).
Sounds like a good compromise between time and trigger started missions. I just hope it is clear when we are under a linear time limit, or when things can wait for a trigger. One of the things which confused me with the first Mass Effect was whether or not I truly had time for side missions, because they were flanked by several extremely important central plot missions. I kept wondering whether I was changing the story, or even hurting my chances, by holding off on those central missions. Part of the confusion stemmed from the fact that it was clear that there was little time to be wasted within the context of the story. Contrary to that, the Council was not concerned to any appropriate level, but it was obvious they were willfully oblivious. As a result, I spread the secondary missions out and ended up missing a few, because once you do all the middle missions you know about it suddenly goes to the final mission which cannot wait. That was a big surprise, because it came without warning and was inconsistent with how the game had played up until that point. In a broader sense it was also inconsistent with other role playing games, where all missions, even supposedly time critical ones, are purely trigger based.
I think those problems could have been easily avoided if a trusted authority within the story clearly states unequivocally that--in Mass Effect--I have all the time I need to do everything I want, so there is no need to rush. That's a very obvious way to do it, and not great writing, but it would have been very useful. A better way would have been to make sure the tone of the story was appropriate to how we were expected to play, although, the point of the game was freedom in how we play the story. One way would have been to start with a smaller mystery that we're interested in following up but which we are not necessarily desperate to follow, either.
Fallout 3 and Oblivion ran into the opposite trouble, where I felt aboslutely no urgency to get to the main story. As a result, I did dozens of side missions before ever doing the main story. I've never actually played either game's story past the third main mission. That resulted in me being absurdly high level by the time I got around to the story, and it completely threw things out of wack--for Oblivion's missions. Fallout 3 suffered in that I had nearly maxed out my experience points, so a large part of the story was missing. I think a big part of that was I simply did not care about the story. BioWare's use of cinematographic practices is a huge part of why I was genuinely interested in going through the main story, I had actual concern for what was going on because it was presented with extreme effectiveness.