Yeah, I don't want to come off as defending single character RPGs, they're shit, outside of competitive PVP games (which I don't have time for anymore).
But cooldowns do make sense, as long as time is a meaningful resource. 5 minute cooldowns wouldn't make sense in a single player game where you could just sit and wait out the 5 minutes. But in a multiplayer online game, time continues ticking no matter what you do and other players can act while your cooldowns are coming back.
So they're more meaningful as limits on your power.
And short cooldowns of a minute or less still make perfect sense in a single player game. It lets the developer say "this ability can be used once or twice a fight","this ability can be used about 5 times a fight", "this ability can be used as much as you want".
It allows for more fine tuning when balancing the game.
Then why even create such overly powerful abilities, if you have to resort to some extremely artificial mechanics to balance them out again?
Because powerful abilities with dramatic effects are more fun. Single character RPGs can get very, very boring if you can only use a few bunch of mundane unspectacular abilities, since the combat is usually not very interesting from an action game perspective or from a tactical perspective.
If you give the player character the ability to do cool stuff like run super fast, vanish into thin air, blind his opponents, go into a berserker rage, break out of crowd control, teleport short distances, shield yourself, guarantee a crit, etc, it makes things more interesting.
But introducing dramatic, powerful abilities can require some sort of additional balancing mechanic. Simply having them take a ton of mana isn't sufficient as a way to balance things; the developer may wish to encourage complex interactions of multiple character abilities. That won't be possible if you run out of mana whenever you use a power ability. Cooldowns allow the developers to say "you can use both of these power abilities together, but you can't spam one power ability over and over".
Which doesn't make any sense at all. What happens with the spells that you suddenly cannot cast? Do you forget them? And if so, why can you suddenly remember them at the next night?
Or are the rituals so complicated that you need the whole night to "prepare" them, so that you can "release" them on demand later? That would mean mages never sleep, or much less than any other person, and that one is pretty hard to believe. This is the most logical approach to the system, and still completely weird and flawed.
If you have learned how to cast a spell (the words, the rituals, whatever), then you can cast it. At any given time, if you have the physical and mental capabilities to do so. Simply logic, common sense. Yeah, mana bars are not too great, but they represent logic better than that Vancian crap. Now, please don't tell me not to apply "real world logic" to fantasy games. A magic system (or any given system) must still make sense in its own universe. And the Vancian one doesn't.
You're right that Vancian magic seems very weird when you try to think about how "it would really work". But I don't care, I just like it because it adds so much thought and planning to the game.
What computer games are there though, where those spells are meaningfully scarce? Every D&D game I care to remember playing allows you to rest so much, that recharging your arsenal between almost every fight that needs it is trivial.
A few stretches of KoTC, a few stretches of the Gold Box games, but yeah, developers are usually lazy and they decide to allow you to rest and regain spells constantly. It's lazy because it makes it a lot easier for developers to balance the encounters, but a lot of the planning and resource management gameplay is lost. Vancian magic does work really well in the P&P setting for which it was designed though.
EDIT: And before anyone gets witty, I know that Vance originally designed his magic system for a book, I'm talking about the guys who later developed and fleshed out that basic idea into a system for P&P RPG magic.