Caveat: I have seen some games, especially store ones possibly rotating attendance, have that the beginning of every session is considered after a long rest. I am not discussing those games here even though I've been part of them.
I wish there were more encounters. I don't want to spend more total time per session. Okay, really what I wish would be a less resource-attrition based model so we didn't need to have more encounters, but baring that redesign I want more encounters.
So what I would quite like, but not as much as that, would be the ability to zoom out a bit - not be as granular with resolution for every task, which just takes time, in a way that gives a good approximation of resources used for battles that aren't big dramatic ones. Basically, if mechanically a combat is unlikely to have a high-stakes outcome (character death, significant campaign setback, significant campaign success, etc) then I'd rather zoom out and do it quicker. This would also reduce the need for "every battle is on-level", a very gamist conceit, if lower-level battles didn't take very long to resolve but still tracked resource usage. And truly meaningful combat encounters would still do high granularity resolution of the current system.
But I don't expect that, either. So I'm kind of stuck with wanting to speed up battles so we get more in a session without sacrificing anything else.