As a separate idea, I very much like how 13th Age does it, but it's too gamist for many people.
13th Age is a d20 game from a lead designer of 3ed and the lead design of 4e. It came out before 5e, but with a lot of the same sensibilities, especially towards streamlining.
Instead of short rest and long rest, they have per-encounter and full-heal-up. Per encounter is what it's written on the tin - as long as there's a gap so it's a separate encounter (no chase scene, or reinforcements, or other ongoing aspect), those come back.
Full-heal-ups, on the other hand, happen every four encounters. Bam. Completely divorced from sleeping or other in-game clock. The GM can have it happen after 3 if some have been particularly hard, and the players can force it at any time, but take a campaign setback. Maybe those cultists have now had enough time to get another part of what they need for their ritual, or the wolves have struck again and more sheep are missing - whatever your adventure it. (As an interesting twist, a campaign setback is also the currency for a safe retreat with all of the bodies, if you can't accomplish it otherwise.)
Because it's a set number of encounters, the balance between the classes is much less dependent on the GM every adventure providing a restricted range of encounters per day. A three week trek across an untamed jumgle might end up being one or two full-heal-ups, or just a morning in a megadungeon.
The idea that recovery is tied to rest is a sacred cow, but one we don't examine often because it has strong narrative sense, though we can accept it more for varying lengths of short rest. So divorcing the full-heal-up from that breaks immersion for some, though the DM can easily put things into the narative for it to make sense such as having that last encounter at the end of the day, just like in 5e they needed to contrive a certain number of encounters per day to satisfy attrition-based gameplay demands. But from a game play perspective 4 encounters then a full heal up works really well.