Also, how would it balance with clerics able to automatically remove the fatigued condition with a touch?
Very nicely, I imagine.
Not that it would change anything fundamental. Barbarians run out of hp; clerics can increase their staying power by healing them. Barbarians get tired; clerics can enhance their staying power by rejuvenating them. Same thing.
But what impact would that really have on play? If the characters are facing multiple encounters that are dangerous enough to merit the use of rage, without having the opportunity to rest, then the barb/cleric combo would be rather helpful (or some wand-using character covering the spells). But how often does that happen? People rest after battles.
To me, the barbarian was designed with the intention that rage was the core ability and that you would be raging at any time that it really mattered. The daily limitation is tangential to any balance considerations. The balance of a barbarian is what can you do in a round when all your stuff is active. Just as the balance of a spellcaster is mostly what can you do with your high level spells.
In the existing paradigm, each additional round of rage you get per day is less valuable than the last, because you only have so many rounds of important action before the whole party will simply rest. It's not a satisfying or useful reward for advancement, and the hypothetical barbarian without rage is something that won't normally happen. So again, how much does just making it fatigue really change things?
Bards play the same tune.
Bardic music is magic. However, it's still a stupid mechanic and I still replaced it. For the enchanting abilities, I simply made them work like some hexes and monster abilities wherein a save makes the target immune for a day. For most of the other stuff, I toned it down and removed the restrictions. Bardic music should just be something you do, not something you have to track.
I would also disagree that there is no purpose. It makes the skill more useful in short burst and for things such as breaking down doors or lifting heavy rocks off of people.
I would agree that my solution doesn't account for short bursts of effort. To me, that's a distinct phenomenon from the berserk state. To rage, one has to get pretty worked up. The idea of it having an on/off switch that the player uses to maximize the utility of rage in a given day irks me. That's not how barbarians think.
I'd rather handle the sudden bursts using a different mechanic, if anything, because they're not the same thing in-game.