Earlier quoted context omitted.
First, where I live (India), libraries are provided by the private sector. So clearly market forces can provided libraries. Second, how much crime is prevented by libraries? Is this the cheapest way to prevent crime? Or would it be cheaper to devote the money to a few more beat cops?
The US library system far supposes India's. There would a few library's near me without public funds. But, most of them would shut down so an equivalent private option does not actually exist. Is it the cheapest way to prevent crime? Is a leading question. Where I live we spend a lot of money on a wide range of things from beat cops to parks and street lights that prevent crime. And library's provide many other servi…
The cost/benefit to evaluate public subsidies is (public benefits) / (public costs). If 90% of the benefits of a library are gained by the users, then it's highly likely that this will be negative.
In such cases, a mixed model is best - i.e., if 10% of the benefits are public, 90% private, then a 10% subsidy for libraries might be justified.