I am not sure what you are saying here.

And I don’t know how stuff works in America, but where I live with most public offers like libraries, public pools, graveyards and stuff like that the amount that the user has to pay is almost never enough to completely fund that thing.

It is still good to demand a certain price, since that increases the appreciation of this public good, decreases wasteful or careless usage and obviously helps to lessen the necessary subsidies from taxpayer money.

I am pretty sure the people enacting those policies understand that perfectly well.

If you would demand so much money from library users to fund the whole library, then noone would use it and a valuable public good would be lost.