Having done exactly this, my main annoyance is that you have to manually power on and off the camera, which means losing whatever zoom and settings you had configured.
There are proper cameras which don't remember settings across power cycles and battery swaps? Curious. Never heard of that before, that's a complete deal-breaker for actually, y'know', using a camera to me. Perhaps the SRAM battery/capacitor in yours is just dead? (Then again, not exactly sure how that happens, I've used 15+ year old Nikon DSLRs and they had no trouble with Alzheimers)
The very first one in the list of recommendations - the a6X00 series.
Theres also the annoyance of actually powering the thing on and off in the first place, which must be near universal. As it is, I use a USB "fake-battery" and just disable that. But its still something I have to manually do instead of the OS just "activating" it.
Some newer compact zooms aren't manual, but zoom by wire. They usually retract when the camera is turned off. This is also the case for most compact cameras, which maybe the GP is talking about, because technically they're also "proper" cameras".
This is actually an issue I've got with the a6300 and the Sony 18-105mm f/4.0 G lens, because it's a zoom-by-wire lens and forgets the zoom setting after every restart.
