3 DPS in a 5-man dungeon would make dungeons too easy and take too much reprogramming. They'd need to nerf DPS output or increase mob HP/DEF. Neither good.

The classes are already uneven.
17 classes/jobs, unless I'm missing one:
Tank- (Glad, Pal), (Mar, War)
Healer- (Cnj, Whm), Sch
DPS- (Lanc, Drag), (Pug, Mnk), (Arch, Brd), (Thm, Blm), (Arcan, Smn)

Group the interchangeable jobs.
Two tank, two healer, five DPS.
22% of queue for tanks and healers each, 56% of queue in one big lineup.

Take your 100 person group and split it into 22 tanks, 22 healers, 56 dps, leaves 34 waiting for another tank-heal duo to drop back.

With my idea, you'd have 22 tanks, 22 healers, 34 dps, 22 "support", you end up with the same dungeons, same classes, same functions, but everyone is grouped right away except 12 people, who will have a 65% shorter wait time than 34 would.

No change except for a shorter wait time.