But it does require residency to vote. Those forced to leave a place due to lack of housing are no longer able to vote, which naturally concentrates the local franchise into the hands of those with higher means.

It helps if you stop modeling the US a democracy where, say, 65% want single payer healthcare and therefore they get it and start modeling it as an oligarchy where, unless the underclasses revolt, people with money and property set policy.

Absolutely and completely wrong. Home owners vote far more and every politician knows it. They're the ones deciding local elections.