It's not just a hypothetical harm, as charter schools in many states have demonstrated. Charter schools get paid by the number of kids they enroll, and they are free from much of the bureaucracy Republicans like to bash so much. All that money mixed with all that freedom hasn't produced much in the way of an education boost: Charter schools perform no better and often much worse than traditional ones. But they have produced a bumper crop of fraudsters.
Do advocates of scrapping the public schools and invoking private school vouchers as panacea actually think that, were Germany and Japan to do the same thing, they would start kicking our asses at math and science even more?
These people don't value an educated populace as necessary to democracy. They don't value the basic human right to learn and understand the universe. They aren't really concerned with improving education at all, they just see public education as a lost opportunity to loot riches.
However effective or ineffective, public education at least carries a moral mission beyond increasing shareholder value.
Privatizing essential public infrastructure is devastating for the people of every country and polity it has ever been inflicted on.