IMO, there should be five different categories of powers:
At Will: we know what this is from 4e.
Encounter: you can use once, and then you have to catch your breath before you can use it again. And, yeah, we know what this is from 4e.
Daily: you can use once, and then have to have a good night's sleep before you can use it again. We know what this is from 4e.
Always On: You activate this power, and it stays on until you turn it off. If you want, you can turn it on or off many times per day/encounter/whatever. (Probably need a rule that you can only have one always-on power at a time, but that you can switch them as a free action on your turn.) A good example would be the 3e Paladin's holy aura power.
Conditional: This power has some trigger condition. Whenever you meet the condition, you can use the power. (Again, you probably need a rule that if you have multiple powers with the same trigger condition, you can only activate one at a time.) A good example would be the Rogue's sneak attack.
I think that covers everything, although I do know 4e did have a couple of "use twice in the encounter" powers. I wasn't a fan. (Also, note that under this model a "class feature" is just a power that you don't get to choose.)
Nah, there are plenty more way to manage resources that are perfectly useable in play and don't hurt your brain the way fighter dailies do.
My favorite 3e example is focus. It was implemented a few times, once as a psionic thing and (IIRC) in PHB II with a set of connected feats.
Anyway the idea was that you attain the proper mental state based on a skill or ritual and then have a small benefit while in that focused state but can also expend it to use a 'big gun' type power. If you want to regain enlightenment in combat it means spending an attack just for the chance. In practice this usually works out to being an encounter power.
But it has several virtues. 1, the static bonus means even if you never use it you don't feel you have wasted the skills/feats/powers that let you buy in to the mechanic. 2, there is a clear and understandable fluff reason for why it works this way. 3, you
can try and use this more than once a combat if you want which adds verisimilitude and gives players more options.
Another way is like in Mike Merles Iron Heros. In that system martial characters gain tokens as they fight based on their actions (and sometimes the enemies) these tokens represent the fighter using his martial skill to manipulate the fight by maneuvering his foes into poor positions, or a berserkers growing rage, etc. You can then expend tokens to accomplish powerful effects.
There are other ways too. For example what if rolling a nat 20, instead of being a critical hit, grants you an "Advantage" token for that fight which might be expended to cause double damage on an attack, or somesuch effect. And could additionally feed into class features/feats/skills etc.
These are all 3e style examples, and I get the feeling 5e is going for a simpler feel than the sometimes compex mechanisms of 3e. I think something as simple as a 'focus' state which can then feed a variety of other mechanics is not an excessive convolution however.
I can tell you that I, personally, would much rather use an Iron Heroes style token system than a "Your fighter can use 'strike of the sleepy eel' once a day" system.
Re: The thread title, this is what happens to me when I need sleep.

Glad you liked it.