Enrage timers exist for two purposes;

1. It prevents healer stacking. You could otherwise bring 3-4 healers to every fight and have a much easier time unless there are harsh dps checks throughout.
2. It necessitates a certain level of DPS. Just as tanks must be able to sustain a certain amount of damage and healers must be able to keep their party alive, DPS must be able to output a certain level of damage within a certain timeframe, while handling mechanics.

To remove enrages removes much of the skill of the game (and is why FFXI HNM was such a joke - yes, I know enrages existed in theory but who the heck took sixty minutes to kill Fafhogg for instance? You'd have to be ridiculously slow).