*Random Thought*
Enrage timers never made sense to me. What is the enemy thinking exactly? "Oh GOD I'm bored... Time to kill these fools so I can take a nap."
If they are just toying with you, choosing to end your life after you fail to entertain them any longer, then why is it when they are about to be defeated that they don't use their full potential? Why die toying with some humans, when you could increase your attack speed, physical damage, magic damage, etc, by 2-3 times?
Silly monsters.
They're trying to find the right aether channel to tap into for their strength boost.
Or, the enrage timer can be more considered a "hard fatigue" on the player character that the boss doesn't experience because it's so massively powerful. Instead of placing a debuff on the character to show this, they increase the boss's power to match the type of situation you'd be in.
... That's all I got.
It's kind of like a Limit Break for the monster. We've infuriated them by surviving against them for so long. I just wish they weren't always one shots or impossible to win against in that state.
It's something that breaks down when closely analyzed, especially if you analyze the very poorly conveyed/executed enrages(lookin' at you, Destiny and FFXIV).
I kind of like Spath's idea of the Hard Fatigue, makes sense, Boss senses you are barely holding on or whatever, goes for the Coup d'grace.