Yes, no, maybe so.
Truth is at least some portion of the cost of living can be included in home prices.
Which gain investment.
Which makes it murkier.
True, although those at the poverty level are unlikely to own homes in higher cost of living areas.
Some on the right argue the red states subsidize the blue states because blue states have higher state income and property taxes which they can deduct from their federal income taxes.
In a reversal of roles I watched a congressional hearing in which Democrats wanted to repeal the $10,000 maximum for those (state tax) deductions imposed in the 2017 tax cuts. The Republicans opposed the repeal arguing it would mainly benefit the wealthy.