This is where you lost me. I don't think "the adventuring day" is a design feature. I think it's a plot element.
I can see that. I expect that a lot of people feel that way. The easiest thing I can say about it is to look at other similar games to see how they work with it, since most of them talk directly to the GM about it.
A D&D "adventure", and this is something that's been in the game since the White Box. Starts with characters having all of their resources. For a long time this meant hit points and spell slots, but we've added more of them since the beginning.
They do a number of things, which you might call scenes, or other people would call encounters. The expectation is that they are going to succeed with them but at some cost. Gradually, over the course of the day, those resources dwindle until the group can't do anymore. Depending on the situation of the adventure, they may be able to stop there, or have to press on.
Eventually, though, the group can't do anymore. We hope they have completed everything they needed to do that was time sensitive by then.
And then they attempt to rest and recover some of those resources. Over time, that recovery has been more automatic and faster, but they need to get those resources back to do more. And more importantly, to do more in a fun way. That's an adventuring day. That's part of the core game loop for D&D.
Over the years, the design of the game has made that more explicit, to the point where you get everything back with a long rest in 5E. That's something that might take a week or more in AD&D.
Way back in the day, this was largely a problem for spellcasters. I remember playing as a low-level magic user and having to portion out my spells over many encounters and not contributing much during most of them. I suppose that's why we have at-will cantrips now.
With 5E, I also play spell-casting characters. I have to figure out how many encounters we're likely to have, how much we need to press on, and how likely we're even going to be able to spend that one hour on a short rest. That's part of the challenge of playing a character with limited resources: knowing when to use them.
I've played with GMs who didn't worry too much about the adventuring day, and that usually meant they were longer. It just meant that I had to be more judicious about using my spells. And that's because the adventuring day is part of the design of the game, part of the core game loop, whether we think about it or not.