Cops in the US are not paid to defend the public. There are Supreme Court cases ruling that e.g. they can in fact just hide behind a door while you're actively being murdered.

I'm not making an argument for or against thr free market, I'm making a an argument about human nature. If we want people not not do something that they see as beneficial for themselves (and the negative effects are not necessarily obvious or are spread enough that they're easy enough to rationalize away), we need to make it so it's not longer so easy to see as purely beneficial. In this case that's likely either policies or laws that prevent it.

The government is just a bunch of people much of the time, and emergent behavior is rampant, so I don't think it's useful to complain about the government doing things we expect them not to when those expectations haven't been clearly communicated through laws or policies. If they have been communicated, then we're looking at corruption, or at best incompetence, both of which we have ways to deal with.