I don't know, dkyle -- how do you define an "adventure" -- it's too fuzzy a term.
I think in the vast majority of cases, it's pretty clear what an "adventure" is.
But "Adventure" is a statement of intent. A DM less comfortable with structuring their campaign with such narrative ideas can set, say, a week of rest to recover "Adventure" resources, and the game would naturally structure around that, without any fuzziness.
These mechanic would enable the same rules to work with both Narrative-focused games, and Simulation-focused games. The Narrative campaign goes with a "when it's logical to the story" rule, the Simulation campaign goes with a set rest period.
Plenty of folks don't play distinct adventures, others play LFR games that are essentially one adventure per session -- and that means there's a lot more variability in the way you build encounters, because it's a lot harder to know how many daily resources the PC can expect to have at their disposal.
Variability between campaigns, sure, but the important thing is predictability for a DM, within a particular campaign. With Daily resources, the players have a lot of agency in when they get them back. They might not rest during the adventure, or they might rest after every combat. Adventure resources are spread across a clear, predictable duration. So Daily resources are more variable, in the way that truly matters.
My ideal is actually that Adventure resources be simply a Hero Points pool, that can be used like Action Points, Healing Surges, and use especially powerful character abilities. This would make it easy to scale how many points for a given campaign structure.
As for no distinct adventures? I'm not talking about adventures as in a Module (I don't use those myself), just a logically grouped set of encounters towards a some kind of goal. I don't think it's common to have campaigns that lack even that.
But really, all that's needed is a notion that resting for a night isn't enough to recover from an infinite number of continuous days of adventuring. If the DM wants a world where adventures do have that kind of unlimited stamina, it would be easy enough to make Adventure = Day. It's less easy to take Daily resources, and split them out into Day and Adventure resources.
I'm curious -- why do you think it would be better to get extended rests less frequently (or the benefits of an extended rest less frequently). I've just said, above, that I do it from time to time for the sake of story and situation, as an exception, but making it the rule? What makes that better?
The main point is to reduce how utterly powerful choosing to take a nights' rest is, because there's no balancing factor built into the game mechanics. I can think of no other player option that is anywhere near as powerful, yet has no real downside or cost defined in the rules. The DM is forced to constantly add his own downsides to try to counterbalance the power of a night's rest. Or rely on metagame expectations that the players won't "game" the system by resting constantly. Neither of which I consider acceptable game design.
The key is that Encounter and Adventure resources aren't player choices. You can't get back Encounter resources during an Encounter without specific abilities to do so, or by withdrawing from the encounter entirely. And it would be the same for Adventure resources.
Now, there is some value in having interesting choices about whether it's a good idea to rest for the night not, so there should be some benefit for it, but previous editions tend to make the decision obvious, because resting gains so much, and loses so little, unless DM fiat declares otherwise.