The problem with "vote with your dollars" is that the more dollars you have, the more votes you end up with. The wealthy can already do this anyway: having those resources means you can live wherever you want, and thanks to the fact that school funding is primarily done via property taxes, the wealthy can move where they like to a school of their choice that will then benefit from that funding.

Unsurprisingly this means schools with a lot of wealthy students already attract other wealthy students due to their successes largely brought about by funding, and poorer schools get even poorer as the few remaining people try their best to leave, because the school sucks.

As I've gotten older I've become incredibly skeptical at the almost knee-jerk reaction to "give people choice and let them self select." What if the choice is difficult? What if it requires knowledge most people don't have? What if people don't need to live with the consequences of the choice? What if the choice affects not only them, but others who have no choice?