The problem with encounter-based design, though, is that it blows up any concept of long-term attrition and thus of parties having to make tough choices between pressing on while down or resting for long enough (overnight? a few days?) to also give the enemy time to refortify and recover. Unless, that is, you make the enemies all short-rest based as well, which could lead to a groundhog-day effect if the party and enemy are evenly matched: fight, both sides retreat, both sides short-rest and recover everything, fight again, both sides retreat, both sides short-rest .....
I'm thinking here of a party comprised of all short-rest classes, which I suspect would quickly become the highly-optimal choice were short-rest classes to be enhanced: the party would simply never run out of gas. Bleah.
By the time they get to Captain America superhero level none of this is much of an issue, but what you're suggesting would affect all the levels below that as well and make a gritty-style game very hard to sustain.