They've never had to run through one of my dungeons. And I don't mean that I kill off a whole lot of player characters. I simply would advise players, at least in my campaigns: if you are in the middle of a dungeon crawl and there are still encounters ahead, you may want to make sure you are not too low on HP. If people are close to dying before they are done with the dungeon, then they'd better have some means of replenishing health before pressing on. Otherwise, it's time to head back, regroup, call it a day, or if a quest is time-sensitive, go seek healing at a local temple or something. I realize, that 5th edition D&D has "healing surges" and such means of replenishing life, but then 5th edition D&D svcks. Give me old school AD&D, 2nd edition or even a campaign with D&D basic Rules Cyclopedia (which many players I know still enjoy) any day. 3rd ed. is kinda okay, but you can keep the other versions.
I think the Fatigue effects thing or health milestones thing sounds like it has potential. At least adding some kind of limited health replenshment ala healing surges would be acceptable depending on how it was implemented.
I have to disagree with the resting thing in DF though. There was the additional consideration of resting safely in Daggerfall (as well as Arena and Morrowind). You couldn't rest when enemies were nearby and you still had to worry about creatures interrupting your rest. Maybe your Daggerfall experience was different, but in my experience, in Daggerfall and Arena both, resource management becomes a big consideration.
You still need potions, and it provides a reason for the health recovery. The player isn't a vampire by default or a troll for that matter. In Skyrim, it's like a dungeon crawl with Master Chief. Where's the Dovakin's MJOLNIR Powered Assault Armor that keeps him alive despite bleeding from countless recent wounds? A troll was once a feared enemy mainly because it constantly regenerated health so was hard to kill. In Skyrim everything, including the player (or mainly the player) regenerates health, so I guess every creature in Skyrim can trace its lineage back to Genghis Troll? Or Master Chief, maybe..?
I don't necessarily think the old way is perfect, but the current system of quick health and mana gen is too easy and makes the Skyrim's gameplay feel too arcade gamey. Maybe it's time for some new ways of handling. I am softening up to the idea of limited "healing surges" outside of combat (but I still don't like 5th ed D&D!) or long term fatigue or health effects, like injuries that only go away after resting/healing.