Another problem is that so-called libertarians are really libertinists. That is they want to be able do every immoral or stupid act but then have the government pay for the consequences. E.g., a motorcyclist, who is not wearing a helmet had an accident and has a terrible head injury. Should the public ambulance provide aid and the hospital provide care? These libertinists have no problem with that. So much for having responsibility for your own body.
Most true libertarians would say there should be no public ambulances or hospitals in the first (which I agree with entirely) place so there is a flaw in your argument
I’d also say no public schools, housing, or anything else of the sort