The 6-8 combats and the classes balanced between daily use, short rest use, and unlimited/at-will usage is one of my biggest issues with 5e. And I'm a large 5e fan. But with playing 3 hours in an evening with lots of RP it requires that any day with combats now is going to be several sessions long in order to balance the number of combats. And realistically, none of the DMs I play with bother.
Mechanically I like the 13th Age system better, but it requires some suspension of disbelief just like the long/short rest options in the DMG, because it uncouples sleeping from regaining all resources.
In 13th Age, resources are at-will (like swinging a sword, or some spells - including ones at higher level than 5e cantrips), per-encounter, or come back at a full heal-up. A full heal-up occurs about once ever 4 combats, though the DM can give it more frequently if the combats are tougher, and the player can take it more frequently but with a campaign setback*.
This means that you could have a three week trip across a savanna that has four encounters total, and that's one full heal-up. It doesn't matter that it took place over an extended period of time, which in standard 5e would greatly favor the classes with lots of daily resources like most casters. I'd describe the trip as biting mosquitoes, bad water and constant threats of beast attack.
On the other hand, if you're elbows deep in a Living Dungeon plowing through encounters, you might get a full heal-up more than once in the same 24 hour period.
This puts to rest the whole 15 minute adventuring day.
Like I mentioned, the DM does have a little more work to keep integrity. Perhaps in the Living Dungeon after the fourth encounter you find a fountain that magically refreshes you when you drink, to keep verisimilitude. It's the same issues that the DMG short/long rest variants have in making it a noticeable milestone. (And, of course, it also gives the DM the chance to occasionally pull out "sorry, timer is ticking and no full heal-up until after you escape the erupting volcano, but that's more powerful for it's rarity.)
Oh, I put a * next to setback. Part of the rules (not just social contract) is that players get a full heal-up sooner, as well as other things like a good retreat if they get in over their heads - but at the cost of a campaign set-back. So maybe they want to rest until sun-up and get an early full heal-up before going after the kidnapped villagers in the vampire nest. But they may find that their delay has let them turn the farmer's daughter into a vamp.