Believe it or not, 4e actually tried this, with its Psionic classes, other than Monk. Those classes used Power Points (PP). ALL of their abilities were at-will effects, which had a stronger, Encounter-like version if you spent a small number of PP ("augment 1" or the like), and a much stronger, Daily-like version if you spent a larger amount of PP ("augment 3" or whatever).
They were generally pretty disliked because they almost always amounted to exactly what you said in the foregoing bit I cut out. That is, you pick your strongest ability and you use it repeatedly until you've solved the problem. And that's exactly the issue with (to use the MMO term) "spammable" resource-based abilities: people will naturally drift to using the most optimal option (or two or three, rarely more than that) every single time, and ignore all other options. This would then truly make most classes "samey," since everyone and their brother would be engaging in basically the same kind of behavior--it's going to be very hard to design that many at-will abilities that can be augmented so.