I've seen far too much unethical and down right illegal behavior by management from inside companies, especially when dealing with privatized government functions, to ever trust them to do anything that they arent forced to (essentially at gun point). While, as an immigrant, I have an extreme distrust of American law enforcement, I would rather them than any private corporation.
I say this as someone who has been on the receiving end of civil asset forfeiture. My grandparents refused to take a bunch of cash that I had brought them in case the economic situation in Russia got worse and was taken for $20k and some priceless family heirlooms on the way back through LAX. It took a year and more money in legal fees than was confiscated just so I could get back some sentimental artefacts.
Nearly everyone I speak with about civil forfeiture thinks it's a bad idea with terrible incentives, so let's just enact some common sense and fix this one little thing, eh?
Even what you describe, limiting the power of government, is a governmental solution. You simply have to elect people who want to make the system better rather than those who want to tear it down. It's easy to say government doesn't work and do nothing.