The Original D&D booklets had the spell slots being used once per adventure. I wonder what that would do to the 15 minute work day?
It would be easier to change the way to regain spells than it would be to change the system to per encounter. You would probably have an easier time simply stating that everyone requires X hours of rest before recuperating spells rather than the flat 24 hrs.
How much it would actually help as far as the 15 min adventuring day, well, that is anyone's guess.
Learning to manage resources properly is a major aspect of mastering the game. Throwing that aside essentially turns the game into a different game. It will also seriously throw off CR estimates since every encounter will be a nova encounter.
I would instead encourage the group to learn to manage their resources more effectively.
Another consideration is that spells are often used outside of encounters and aren't always appropriate for combat. Comprehend Languages, Read Magic, Floating Disc, etc.
If you wanted to further constrain casters beyond spells per day, maybe you'd want to explore a limited number of spell levels that could be cast per encounter, and as a PC advances, that level limit expands. But, I'm guessing that your intent is the opposite, in that you want casters casting more spells, not less.