The government usually provide little service, but the state do. The question whether you trust it as a single entity is a bit hard to understand. Do you mean trust that my father gets his pension? Or that my kids get a good education? Or that my neighbor who is a doctor can provide decent health care?

I probably trust some of those more and some less, depending on the circumstance. But basing trust on funding model seems intellectually .. challenging. Would I trust a university teacher more if the employer is not a state university? Would I trust a policeman more if working for a private security company?

Not likely. Trust is based on other factors, including reputation and competence.