I don't know about your state, but in my state, rich people have influence at the state level too.

It doesn't seem axiomatic to me that rich people will always exist (I'm not sure I even agree that poor people will always exist, despite believing that the guy who most famously said it was divine), and one of the things I have learned from working in an industry with very rich people is that merely being rich is enough to let you influence the rules of the game. If someone was able to argue for tiered zoning, you can pay people to argue for un-tiered zoning. If there's a law preventing you from influencing local zoning, and you're rich, you can go change that law just as easily as it got created. If there's a law requiring certain representation on zoning boards, you can go lobby that representation. If there's a law moving zoning to an "apolitical" government agency, you can fund candidates willing to politicize it. And so forth.

Making people not have that level of influence/leverage in the first place, hard as it might be, seems like the only viable solution.