If it's assumed that days end at the end of a session, I think that assumption itself needs to be examined.
Each round of combat is, what? 6 seconds? 5? And how long are combat encounters lasting? 5 rounds?
The average battle lasts 20 - 60 seconds in world, but can take as many minutes at the table. So, if you spent the entire session in combat, you're looking at 3 - 5 minutes out of the characters' day.
Unless there's an in-game reason for it, days don't need to end at session end, and should carry over.
Rough resting is a good system, but it's nice letting casters get their spells back while you're roughing it. And if game days stretch across multiple seasons, there isn't as strong a need to penalize the casters. A compromise here may be Pathfinder 2 style "rests", where players get their daily abilities refreshed, but they don't regain more than a handful of hit points.
Force them to use those lower level spell slots on heals between combats, or eat up potions.