That's fair enough to some extent. Not sure about the US, but in the UK they are also responsible for re-securing the access point when they leave, and I believe you can claim compensation for the repair work. Presumably also, if there were any thefts while the property was in this vulnerable state, the insurance company would sue the police to try to reclaim the money paid out to cover the loss.
Taking someone's primary mode of transport, perhaps their only viable option, is a whole order of magnitude worse than breaking into a property to carry out a search warrant. For someone who's not even a suspect, or in any way connected, it's a massive violation of their rights.
> only tow the car if they can't contact the owner, which seems consistent with that
To be honest, it seems unlikely they'd easily be able to contact the owner, unless it happens to be parked outside their own residence. And the flip side of them not being able to contact the owner to ask permission is that the owner has absolutely no idea where their car is, and they only find out it's missing when they need it most. And probably not in an area they'd like to hang around too long in, if there's just been a homicide near there.