Bards don't have more mobility in some sense, they have more mobility in ALL sense. The fact that monks HAVE to move to maximize their dps actually RESTRICTS their mobility. Monks, and melee in general, also have a bunch of extra mechanics to deal with that bards never will, mechanics that can make people just not bring melee so they don't have to deal with it. SE seems to be doing a better job at balancing this out but melees will always have more crap to deal with, just part of the job.

People do not fight over Monks for their "insane DPS." Yes, Monks have the best single target dps and 2nd or 3rd best AoE dps, but a lot of people fail at Monk. Also, their extra DPS will rarely ever make or break the fight because other DPS are perfectly able to beat any DPS race mechanics. Also, Bard can bring more effective AoE dps through their songs even though they actually have the worse personal AoE dps.

Bards are desired in every group; they are not REQUIRED (no fight in the game requires a Bard) but they provide a very very nice safety net. Having a healer revive at 0 MP is a very bad thing indeed.