I’m curious that you think that no one would provide parks and libraries (or “proper” ones, anyway). It’s a good thing people have decided to provide us with amusement parks, theaters, concert venues. I’d hate to go to a government-run movie theater. (There are any number of privately run libraries that will admit all comers; ditto parks.)
I think that the proper functions of government are:
To prevent or preclude the use of force and fraud against its citizens—that is, to prevent us from doing those things to each other, and to prevent foreign governments (and individuals) from doing that to us, too. So I do believe in a system of courts, police and prosecutors and a robust national defense.
To set up a system of standardized weights and measures and enforce adherence to those units and standards. That’s really about as far as I think “regulation” should go. Things advertised and offered for sale should contain the contents as advertised, and no more or less. (Poisonous or adulterated products and faulty products sold without warranty or recourse would be covered under the first point I made.)
Government may be required for some, maybe even most, large scale civil works projects, such as building and standardizing roads, ports, railroads, airports, canals and the like. I think the time has probably passed when we could experiment with this being done “privately”, but I wish we had tried more of this in the past. (I do not think we need more government involvement in building sports venues. How this always seems to pass muster is beyond my comprehension.)
In most cases I think that if a thing is too important to be overlooked, then we should have no government involvement in it. Supermarkets, for example. I’m glad I don’t have to go to the Post Office for my daily bread…
PS: I think mail delivery should be privatized, too. The government may have an interest in ensuring that everyone can have delivery, but they ought not to be running the business.