IMO the (short) answer to that problem is more dungeons. Once you leave the dungeon to take a long rest, the dungeon won't be waiting for you passively. Its residents are now alert they are being invaded and muster defenses, set new traps or even hunt you outside the dungeon. Thus, once you delve into the dungeon you have one adventuring day to accomplish your objectives, because once you leave it and recover your energy, so the dungeon does.
E.g: The last dungeon my players invaded was a thieves' guildhouse. Their objective was to either capture the thieves' leader. They knew once they were spotted inside the guildhouse they wouldn't have a chance to try again later and had to press until the end, because their leader would be hiding somewhere else if she knew she was being hunted and her hideout was revealed;
It works for a specific kind of game, but it works well.
Edit: Additional note. Not every situation is a "one try only" kind of situation. When delving into ancient ruins searching for treasure or with an objective in mind, for example, doing it "one encounter per day" shouldn't make it easier. Instead, it should make your job harder, since you're giving the underworld time to react to your strategy. So, once you delve into the dungeon again, you're not as close to accomplishing your objectives as you were last time you left the dungeon, but it's still feasible.
Only working in specific situations is a big part of the issue. The DM shouldn't have to do special work or make narrative decisions to make the mechanics of the game work. The mechanics should support the narratives. We shouldn't have to say, "Well, I need to structure the story this way or else I'll run into adventure day XP budget problems." I think that's an indication that the game is foundationally broken in a pretty significant way.
The problem here is, what do you do when you're running a dungeon with more than 8 encounters? Rappan Athuk is workable because of the nearby town, but there's no way you're retreating all the way to Hommlett while you're going through Castle Amber, Temple of Elemental Evil, Demonweb Pits, or Undermountain. Even 5e adventures like Storm Kings Thunder, Descent to Avernus, Out of the Abyss, or Rime of the Frost Maiden don't really work like that. You often can't withdraw and long rest because
there's nowhere to go. If you need to long rest -- and I think the module authors assume you will -- you've got to hole-up in place. Think of how many adventures there are where the PCs go through a portal, end up on another plane, and are then
stuck there until the end of the adventure when they can finally escape.
I did not say constant, did I.
No, I did. Under the assumption that if you want the issue you're trying to fix to
stay fixed, then you can't eliminate it without the same issue returning. Having a solution to a problem that only works some of the time is not particularly compelling.
well, I was more referring to the HPs, despite quoting both, but yes, if you consider HP your physical fitness then you won’t perform great feats while you are exhausted / injured, so they are tied to that too
You're no less able to pass a skill check at 1 hp compared to max hp. That's about as realistic as a fireball.
nothing wrong with the mechanics supporting this, but you getting stronger / gaining abilities as you fight / progress during the day is not the solution to me.
That's only
one possible solution. The point is to reward the players for progress, not do exactly the first thing I happen to suggest. The point is that narrative solutions require you to twist the game. They limit your options as a DM, or require you to repeatedly punish the players when all they're doing is literally reading what the book tells them and making the most logical decision. It's a bad design.
A
better solution would be to eliminate "daily" powers entirely, and instead do what nearly every other TTRPG does. Have limited use abilities recover per scene or per set of scenes. Recovery can be automatic at the start of new scenes, or at a fixed rate of in-game time that is significantly divorced from health recovery.
A boxer does not suddenly go all out in round 7 and perform at a better level than in rounds 2 and 3. A marathon runner does not have their fastest mile at around mile 20…
No, but the first round is seldom the most dramatic or exciting, and the first mile is rarely the fastest, either.
One of the goal for a DM is to setup challenging and satisfying fights for his players. The xp budget is a tool to help that.
We should not use the reverse view : the goal of the Dm is to respect the xp budget and use fights to fill the budget!
No, that sounds nice but that logic leads us to the conclusion that there is no problem if the PCs long rest after every encounter. The difference in the design of Fighter and Wizard pretty significantly contradicts that.