I float a scope around from time to time. There's no reason not to - whether it's for load development, carried as a backup, or just for troubleshooting.
I keep (admittedly shoddy) records, but each rifle has a book. I endeavour to keep a running shot count, but focus more on POI. Keeping DOPE for different loads allows me to switch ammo without having to sight in every time.
Same goes for a scope. After you swap it over, just record how many clicks it took to zero.
After many years of 'lesser' mounts I've been pleasantly suprised how consistently Seekins and Near hardware perform for me. I havent used everything, im not saying 'mine are best', but I have moved a scope from one rifle, to another and back, dialed the correction and confirmed my zero. More than once.
Given your choice I would rather share a good scope and invest in quality hardware, but I'm likely in the minority.
I wouldn't recommend it if you don't have a torque wrench, or only have one scope though...