Certainly not being able to do all of them is annoying, or the stupid 6 hours you lose just going into the world map makes a huge difference about in-academy quests and town quests. I don't know how this was a good idea.
Doesn't make it any better--if anything it only makes it worse--but the guide mentions fifty bazillion times that the game was DESIGNED
to be played multiple times.
To be slightly more specific, time limits for free time become a lot easier to manage on a second playthrough because all the scenes that you viewed before do not take up any time. Further the expert trials have recommended levels that correspond to about what your level is expected to be for the new game+ exclusive missions for the corresponding chapter.
Edit: Another tip, for missions like "Kill X number of enemies using (magic spell)" you can complete the mission in the arena to save six hours.