I think one of the bigger changes, and this has been touched on, that DM's need to incorporate is that HP are now a strategic level - ie encounter - resource, not a logistical one. HP are a way of controlling pacing and strategy in combat. But, between combat? No, not really. It's typically trivially easy to restore everyone to full HP repeatedly during an adventuring day.
This is largely due to the way 3e played and has continued since then. If you had a group with wands of cure light wounds, then HP attrition vanishes as a resource to be managed. You just have such an enormous pool of HP that you may as well just hand wave it and say you start with full HP in every encounter, because that's the way it's going to play out.
5e is largely the same. HP are not a logistical resource. They just aren't. And trying to make them a logistical resource - by changing rest periods, interupting long rests and whatnot, largely is rowing against the current. The players just have SO MANY resources at their disposal - from cheap healing potions to the fact that probably at least half the group can cast healing spells - that it really doesn't matter.
IMO, it's a better solution to simply go a different direction. Stop trying to make HP a logistical resource. Personally, I favor the idea of fatigue. Every rest, make a scaling Con save (or whatever). First rest, DC 5. Second rest DC 7, so on and so forth. Every time you fail, you gain a level of exhaustion. DC's only reset after a week of rest. A single long rest, while restoring HP and spells, and obviously reducing one level of exhaustion, doesn't reset the DC's.
Now, you have a nice little logistical mechanic that pushes the players to push forward and not rest after every encounter.