Enrage timers stop people wasting hours on something they just can't beat. Ever hear about the LS in FFXI that spent 20 hours trying to beat a boss? SE got huge backlash for that (even though it was the players' own fault for taking it that far) and they ended up putting a 2 hour(?) timer on that fight.

FFXIV isnt that difficult, and it'd eventually come down to bosses being slowly wittled down to death, or healers running out of MP (but there are easy ways to restore it) so really, it would just remove any challenge from it if there werent enrages.