Well, really. There is one big, gigantic problem on time limits. You completely skip all the content when you have a timer ticking on you.
Recently I did Toto-Rak for the first time, I had the major luck of having a party of L50s with endgame gear assisting my poor cute L25 noob tail, we were blazing fights so goddamn fast I didn't had time to land a single auto-attack with my LNC. I didn't even feel the boss fight so fast it rushed past. Yet, I didn't stop to read a single sign. I skipped past the moogle's text (hunted it in the chatscreen after we defeated the boss). We made a near-perfect run for the hardest boss, we missed exactly two photocells, which added about 5 minutes to our time spent. We finished with 20 minutes left. And you know what, i'm still goddamn curious about what the hell is going on I have no idea about what the inside of Toto-Rak is... The ACTUAL content, I skipped so we could finish it, and that's because we were on easy mode.

That said, I do not disagree with giving better prizes for people who ace a dungeon! Having a timer that determines the quality of your loot by the end would be pretty ace, but a timer that FORCES you to be booted out of the dungeon after a while will simply make you skip any actual content inside. (though it is a neat idea in that the developers force themselves to make a dungeon that can be completed in a decent amount of time if you don't dally)

So i'd be more for a timerless dungeon, or rather, one with a loot timer instead. Or if you REALLY need to make a dungeon with timers, do it plain and content-less because players are going to skip the goddamn content anyway.