text of D&D, the Vancian mechanic is defining. In another rpg, it might not be, but D&D magic generally has a per-day component. Nonmagical things generally do not have daily limitations in D&D
Meh. In classic D&D, /lots/ of things had x/day (or week or month or whatever) limits, not just magical things. Almost anything that had a limit, really. Fighters didn't really get any of those things, because they didn't really get /anything/, sure, but it was a common abstraction for 'this doesn't get used all the time.'
Vancian magic is legitimate, but the key to Vancian isn't so much the per-day aspect as the memorization aspect, which even 4e retained for the wizard (and only the wizard).
(no, hit points and healing are not a daily mechanic)
In what way is a resource that can be renewed on a daily basis not a daily mechanic? Each healing surge can be used once each day.
, which is why the exceptions (i.e. Bo9S, the PHBII knight, or all of 4e) are referred to as spells, again specifically in a D&D context.
Well, it's an understandable shorthand, but a loaded one, since calling a non-magical ability (whether 3.x Barbarian Rage, which was explicitly an extraordinary ability, not a supernatural one, or 4e exploits, which were explicitly /not/ supernatural abilities, even though they could be super-human at higher levels) a 'spell' implies a clear contradiction. One that is being added by the choice of the speaker to use the word 'spell,' not by the system.
It's also worth noting that in the specific case in point, the mechanic doesn't represent any kind of fatigue
It doesn't represent anything specific. Only the wizard, in 4e, has an explanation implied for some of his powers being daily. For everyone else, it's left open.
Lastly, consider why the power system was conceived in the first place: to try to balance characters with spells against characters without spells. The underlying intent was to make martial exploits and spells balanced, and the same supernatural-sounding terminology (powers) is used to describe both.
'Powers' is a general game term, but each source had it's own specific term, as well, that emphasized that they were not all supernatural. 'Power' is not strongly super-natural. Electricity is commonly called 'power,' a physically strong person is called 'powerful,' someone with a good memory is said to have 'remarkable powers of recall,' and so forth.
Maybe having played Hero for a long time de-sensitized me to any connotation of 'powers,' too, because in Hero, you can use a 'power,' like an EB or KA to design anything from a supernatural lightning bolt to a martial arts technique to an ordinary firearm or even just a club.
So this equivalency is not something that some ENWorlders made up out of nowhere; it really derives naturally from what the 4e designers wrote.
The common mechanic of powers is real, enough, but it implies nothing about the nature of powers - powers can be granted by martial skill, by divine dispensation, by arcane magic, by racial talent, by magic items, by boons granted by greater powers, and so forth. Even a simple 'Melee Basic Attack' is a power.
he conclusion that power implies that exploits are supernatural is, indeed, something that exists only in the minds of those groping about for something about 4e to hate. The 4e, PH, itself, explicitly states that exploits are not supernatural.