Some public schools that we have right now aren't working well (ie, the implementation is a problem, not the idea), because we have, for decades, been siphoning money away from them to fund private schools, refusing to provide funding for necessary materials (textbooks, classroom supplies, building maintenance, desks & chairs that don't break when you sit in them), underpaying and under-hiring teachers so that many people who want to go into teaching feel that they can't because it's unaffordable...

Just "throwing money at them" isn't going to work, no, because the money needs to go to the right places. But there are so many places where it's pretty clear that extra money will make a huge difference that arguing that schools are overfunded—or that "public schools don't work"—is just ludicrous.