Aside from Vance and D&D (the game, related fiction, and direct ripoffs of same), are there any other RPGs or fiction where powers are commonly limited on a "uses per day" basis?
Fairy tales, maybe; but even then, it seems to me that it's usually more like "once per year" or the like, rather than "once per day" (let alone "once per day, must have 8 hours of rest, followed by 15-60 minutes of prayer/study/meditation before recovery).
There's the Midkemia books, where lesser wizards are so limited -- but they *are* D&D wizards (Midkemia was a group's D&D world), and they quickly get ignored in favor of the greater magic wielders, who don't have that limitation.
Even the Vlad Taltos novels, which are also (very loosely) based on a D&D game, don't have "per day" abilities, IIRC.
IIRC, in the later Amber books, Merlin comes up with a method of "hanging" spells, which works out a lot like D&D-style magic -- but there are plenty of other potent abilities around that don't have that limitation.
Lots of games and fiction have powers & abilities that tire the user, which leads to said abilities not being used often -- once a day, and then done. But the users are then *tired*, and can't continue to merrily tramp along shooting their crossbow. They have to actually rest -- and they generally don't have to wait until the next day, either.
In GURPS, you rest for an hour or so at max, and the spellcasters are good to go. You have to leave & rest when everybody's beat up, and already been healed enough such that the heal spells are likely to fail or critically fail, and maybe it's time to fall back. But that point might never come, if the players are smart and the characters sufficiently skilled/heavily armored.
In other games, you can run out of spell points/mana/whatever -- but a lot of them _don't_ have "recover them all at once, once per day" rules. You get back some amount over time -- so you can just rest the requisite time, and then get back at it. Exalted, for example -- the Dawn caste can blow all her Essence on one fight, then nap for a couple of hours and be semi-functional.
So why is it so important? In one sense, it isn't; it's just a game. In another sense, it is because it doesn't let me play a game that's like anything but D&D fiction.
(And plenty of D&D books don't seem to play by the rules, either. The spellcasters either get physically worn out, or they just never seem to run out of spells until it's dramatically appropriate. Curious, that.)