I think the idea is that if one plays the game naturally then it's one and the same: mission time will advance alongside the story timeline. However, having it based on real time instead of missions completed allows OCD players the opportunity to make sure they've done all the side advisors missions before advancing to the next section of the game, which will then unlock more. So I do think it supports different styles of play a little better.
Meaning that without the timer the adviser missions would only complete after, say, another critical path mission? So if you failed to launch the adviser missions in the right order you'd be in trouble?
Mechanically, this reminds me a bit of ME3. You've got a bunch of galaxy map stuff available --side missions, fetch quests and scanning -- which pay off in cash, upgrades, XP, Rep points, and WA points. Most of the payoff from the map is in WA points, but it doesn't really matter if you get all of those right away since they don't do anything until the endgame. The other stuff is nice, but not unbalancing. If most of your upgrades came from the map, I can see how pacing it out would be a good idea.
(Possible exception for Rep points, since in a non-import game I don't believe you can pass the important dialogue skill checks without the galaxy map points. But hopefully ME3's persuasion system is not relevant to DAI. )