Makes sense. Seems like the incentives will be problematic either way.
Personally, I'd just have the state cover it, but explicitly not have it come out of the police budget. A reimbursement check or tax credit could work.
In the event that malice is suspected on the part of any involved party (police department, property owner, 911 caller, home invader, etc.), it would be on the state to press charges and recoup its loss.
My home insurance would cover police damage unless I was the person they were after. It’s still likely I would have to cover the deductible. You could probably take the presumed criminal neighbor to small claims court and try to get back the deductible. I’d bet any decent judge would be sympathetic to the home owner.
We had a SWAT team destroy a fence with an armored vehicle during a standoff and they were just like, "not my problem."
Apparently they don't want to have to make decisions based on cost.