Of course there are limits on what can be achieved. But we won't know until we try. It's hard to be worse than the current system of no incentive whatsoever.
Where did you get the idea that US public schools are in some kind of crisis? They're doing pretty well, like they always have, but people are remarkably willing to simply accept claims (often by parties with financial interests in making them) that they aren't.
This is hardly ever true, for any kind of system.