That's not a analogous scenario though, because a) afaik police still need a warrant for a battering ram, they can't just enter, and b) battering rams are kind of a 1 time thing and very very obvious. The key is more like the police can just let themselves in at any time to check that there's no dv going on. If you're not home you don't even know if they were there. And incidentally some silverware has gone missing... That's closer to the scenario we're talking about.
Actually I'm in UK although it might be the same here. Second point still stands though: you can't tell if someone has been into your house.
Edit: to elaborate on "the silverware", "the police" having access means effectively anyone has access. It's not just 1 infallible person, you're giving that key to the whole station, and it's being kept somewhere, which makes it (more) vulnerable to theft, especially since a large cache of such keys is going to be much more attractive to a criminal than a single key.
