In fact when it comes to schools I am the someone else paying for it, because my children aren't in every school at all times. And I'm fine with it.
I frankly find this attitude that social benefits should be pushed back on because not everyone is partaking in the social benefit at the same time to be frankly hypocritical to communicate on the internet, a technology I certainly didn't pay the salaries of the mathematicians and engineers for.
They very clearly meant “you don’t have to pay at time of use, it’s paid by tax dollars”, and nearly everyone who reads that comment would interpret it that way. There’s no reason to pick the dumbest, most braindead interpretations of such comments just to make yourself feel smart. You could have just thought “they probably mean taxpayer-paid” and then moved on.
So you suggest we pay them with what, exactly?
With gold coins? With fruits harvested from the vast fields of money trees?
Or maybe with the collective consensus illusion of funds fabricated by "government" for the use of its citizens?
Money isn't a real thing. Money is not a real thing. There is no such thing as money.
Public services can be paid for with the same thing everything else is paid for: the surrounding social system ("government") saying that it's paid.
People are so deeply invested and locked into maintaining their grasp of the illusion of how things really are that they cannot fathom "the way things are" is completely invented and almost always subject to change if people would just stop maintaining the illusion.