I ran the Apple Enterprise account for a municipality in Denmark. I don't usually have a work device, partly because I don't want to bother with the taxation rules but mainly because I just don't want two devices.
Anyway, what I did was that I got our IT department to create an Apple account that wasn't exactly tied to a specific person and use that to create the municipality owner account. You'll have to go through Apple verification which involves real world phone class, but once we were done with that process, I added my own account with admin rights. This way I didn't have the issue of not having a "work" device while also making sure the municipality would keep owner rights with no issues if I died.
I think our biggest issue was actually the payment. Usually you won't want to tie a credit card to enterprise payments because credit cards run out, but with Apple we had to. So we had to set up alarms and stuff to remind IT to renew it.
Ideally you wouldn't want to do much of that, but unless Apple has changed their ways they are still just terrible at selling products to enterprise and you'll likely have to make do. Just make sure the "owner" account isn't a personal account that can't be transferred when an employee leaves.