It is a much more systemically flawed situation, because it is a positive feedback loop - and it isn't even really about money.
Good teachers want to teach students that want to learn, and they don't want to be bogged down by the failures of less popular schools (we are holding off on income for a bit here). They end up moving where schools are doing a better job, mainly because the culture of the region has parents and children who value their education. They get paid more, because the school wants to retain these better teachers, who do good jobs, rather than the assembly line college graduates who ended up in education as the "default" and just want the job security.
So now money can factor in, and these better teachers with proper facilities are being paid more, and have better maintained institutions to keep them hired, and since the region already has a pro-education culture in advance, it has wealthy people who pay higher property taxes to keep the school all the more well off.
And just equalizing the money doesn't kill off one half of the feedback loop - it just renders one neutral. Good teachers would still go where parents culturally want their children to learn and promote their educations rather than places where the parents, and by extension children, predominately don't like the education system and are hostile to it.
Fundamentally, the solution is that every child needs to simultaneously want to learn, more importantly learn something they can be passionate about and pursue as a career (besides basic human interaction like arithmetic, grammar, essential history, and things not taught in school like how to calculate taxes, essential law code, etc) while at the same time they are paired with educators who give them the one on one engagement to keep them on track, who value their role as the builders of a future generation more than their guaranteed paychecks, and getting those two to pervasively penetrate culture is a much bigger problem than moving money around.