When I see abilities that are X times per day, I understand the intent of the design as modeling something that is extremely taxing/fatiguing to do. However, I don't think is does a convincing job of communicating that intent. X times per day is either (a) metagame logic that doesnt map to any kind of in-game narrative, or (b) an easy way out for the designer.
Metagame logic can work if the rest of the game is designed around the use of resource points to model some sort of genre, but D&D isn't one of the game systems anybody associates with that. For example, D&D casters have a story behind them - they literally forget spells after casting them - that explains the daily limit on spells and the need to rest and study to recall spells.
I guess I've always seen these as balancing limitations first with no real explanation for them. The way I see this is like this:
"So, wizards can only cast a couple of spells per day to balance them."
"But WHY can the only cast a couple of spells per day in the game world?"
"There isn't a reason. It's for balance purposes."
"That's not good enough, I want a reason!"
"Fine... they... umm... forget the spells after they cast them requiring them to rememorize them the next day"
"Awesome."
"This fighter power needs to be limited, allowing them to use it constantly would be very overpowered but the class is kind of bland and boring unless we give them a couple of powerful options to use."
"Great! Why in the game world are fighters limited to the number of times they can use this?"
"There's no reason. It's a balancing method to the game."
"That's not good enough, what's the reason?"
"Umm... I got nothing. Sorry, can't come up with a reason but the game would suck if we removed those powers and would be overpowered if we allowed them at will. Guess you'll just have to ignore the fact that there's no reason."
To me, the entirety of D&D HAS been designed with metagame resources. Things like spells, god granted abilities, and magic items. They've just come up with an adequate(and I only say adequate since it's not a very good one) reason to justify the metagame resources for spells because it's easy to do so. Magic doesn't really exist so people are willing to accept nearly any justification. That doesn't really make the resources any less metagame. They just have a thin coating of honey on them to make them go down smoothly.