Not in a criminal court, or really anything where the government is the counterparty. Philosophically it’s because those things are part of your “civic duty” as a citizen like taxes. Realistically it’s because the demographics of people getting the money would be unpalatable to the public. Recidivism is high, some large portion of it would go to people with prior convictions.
The absurd end of this spectrum is what happens when police damage a random persons property while chasing a suspect. They’re generally not liable for it, however most homeowners insurance won’t cover it.
I remember an early GoFundMe from a lady that went to work and a guy broke into her house and had a shootout with the police. She came home to being homeless (house got condemned because plumbing, gas, etc is bullet-riddled), and it’s a really disconcerting story to hear. I don’t recall if the city settled to quiet the story down or not.
The "civic duty" rationalization is bunk, due to how unevenly it ends up applying. Someone having their house destroyed is not a "civic duty". Everyone's taxes going up a few dollars to compensate for the damage the police caused (to a house or otherwise) would be a civic duty, and municipalities paying the full cost of policing would place responsibility where responsibility belongs.
I completely agree about the realpolitik reasons though. Ultimately we need out of touch voters to realize that unaccountable government can easily turn its sights on them, as well. The real difficulty is trying to make people respect numerically low odds without falling for feel-good nonsense about "those people".