This is true, but misses the main point for how to determine whether the government providing money is better than not: positive externalities.
As an example, we all benefit hugely from the existence of an EMS (911, ambulances, emergency rooms) system, even if most of us don't use it much. That's a positive externality that's worth the government making sure happens, as it wouldn't necessarily happen without government involvement.
Similarly, public schooling (or publicly paid school) provides externalities: a literate society, a basic level of civic and cultural knowledge that people can assume as a baseline, opportunities for social mobility. None of those exist with a voluntary system.
This proposal doesn't seem to pass that test: at least, nobody has proposed positive externalities that come out of this.
As an example, we all benefit hugely from the existence of an EMS (911, ambulances, emergency rooms) system, even if most of us don't use it much. That's a positive externality that's worth the government making sure happens, as it wouldn't necessarily happen without government involvement.
Similarly, public schooling (or publicly paid school) provides externalities: a literate society, a basic level of civic and cultural knowledge that people can assume as a baseline, opportunities for social mobility. None of those exist with a voluntary system.
This proposal doesn't seem to pass that test: at least, nobody has proposed positive externalities that come out of this.