Actually there are lots of times that a lightly armored APC comes in real handy in a stand off situation. They work great if you have to go in and rescue civilians and/or wounded out from the line of fire.
North hollywood shoot out for one. Several times they tried to rescue wounded people and were beat back by the robbers overwhelming firepower.
Of course, there is already a vehicle in production that fits the bill. Money transport armored truck or van.
Were I the police chief and the SWAT commander wanted an APC, I'd kick him in the jimmy and make him requsisition one of these
High front bumper for ramming gates, running boards for deploying swat police in a hurry. And the first person that tried to mount a machine gun on it would get said machine gun inserted rectally.
Utah county SWAT van
Perfect use of police dollars there.
This, however, is *expletive deleted*ing insane