And also, like basically everything in the game; it's an abstraction for the purposes of the game. A game with limited ways to present discreet powers because spells ate everything forever apparently.
Yes, mechanically, it's per rest (preferably short as I feel that per day resources should be SHARPLY limited), but in-universe it's because you're having to wait for an opening to allow it to happen and once you execute it, enemies that watched it happen will be on guard for it.
Additionally, per-encounter powers have two purposes:
1) to limit on abilities too powerful to be at-will
2) enforcing variety in abilities and tactics.
I often take note of what is actually attributed to 2 and give those options to recharge on an encounter.
As for risk/reward mechanics, the issue you're going to run into is several-fold:
1) It's difficult to standardize with any variety.
What you'd need is a rather robust set of conditions to proc off of their use. Otherwise, you're going to just get random penalties applied to risks, which runs into the problem of...
2) Designers are people.
And... that's a lot of work to put on people to make a whole system on the order of spells with absolutely none of the standardization, structure, and shortcuts of spells. And that's impacted by...
3) Limited Design Space
Same old song: Disadvantage or Exhaustion there's precocious little more in 5e to actually work as a design lever. And because I see a dozen hands racing toward the 'exhaustion button...
4) Caster-Favored Death Spirals.
Exhaustion is not a good mechanic. In fact, Risk/Reward mechanics as presented... are also not good mechanics.
Look, as DMs, we love conflict and adversity. It's drama. It's conflict. It looks really good in the book we're writing in our heads moments before the first player decides it's time to spend ten minutes harassing a squirrel.
But the reality is this is a game of math and very limited math at that. a mechanical penalty means drastically increased failure. And exhaustion not only imposes mechanical penalties, but just straight up kills characters for having it. Risk/Reward mechanics is basically just gambling on making your character just plain worse.
Annnnd we're specifically saddling the martial classes with making themselves worse to try to do things while casters just don't. They get to use resources with the only onerous limits put on them being the DM looking s/mad at them when they has a Tiny Hut, thus eliminating annoying and time-wasting random encounters forever.
Which is sort of hilarious when in certain pop culture, it's the mage that's supposed to be stabbing themselves and paying in their own blood for power.