You ever work in the kind of shop where they don't know if their stuff will survive a reboot?
Yep. professional environments and even my home stuff I don't like rebooting because of that. It's rare for stuff to fail at random, typically it fails on shutdown/powerup. I rather not touch it if I don't have to. That's why I have 4 100AH lead acid batteries. That's still not enough imo, I want to redesign my system into a proper pure sine dual conversion setup as standby UPSes can still introduces brownouts to the equipment and I've suffered reboots a few times already because of that. Dirty power outages where it's not a clean cut wreck havoc on the equipment as the UPS does not catch it fast enough.
That said, I think the risk of a failure during a physical move is high enough that I would personally shut down everything. When I did some power upgrades years back to my rack I technically could have tried to find a way to do it live including transferring to new UPS (Very careful live wire splicing basically) but the risk was that a wrong bad move could cause a full rack hard shutdown which would be more damaging than if I properly shut everything down.