@Yaarel has a rather cool alternate resource recovery mechanic noticing the number of challenge encounters (of any type) needed for each level, and then making all rests short rests, but a (low) number of times per level allowing a character to treat it as a long rest. It more closely matches designer expectations of number of encounters per day, and he had a good narrative work-in as well.
While we both agree that it is overcoming challenges that should lead eventually to leveling regardless if they are overcome by combat, I'm being a perfectionist in the I would rather tie the resource recovery not to any type of challenge, but specifically to combat encounters because the resource attrition during them is much higher than we regularly see in other types of solutions. I've been spoiled a bit by 13th Age, where classes are calibrated for four encounters per "full-heal-up" (read: long rest), and the resource mechanism is literally four encounters. It lacks the narrative connection of either the current long rest mechanic or Yaarel's replacement, but from a game perspective it can't be beat.
Yaarel's solution is quite elegant, but we've been going around a bit in circles on recovery with fewer combat encounters because non-combat successes also contribute to leveling, and for me if I am going to upend the whole rest cycle mechanic I really want something that focuses just on the heavy resource expenditures.
(Yaarel, please correct me if I've misrepresented anything, not trying to put words in your mouth, just trying to explain to someone jumping in late what's going on as I see it.)