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my suspicion would be that more equitable wealth distribution would make housing even more expensive

in some scenarious even taxing third homes could ultimately reduce the supply of housing

a land value tax on the other hand...

Why would equitable wealth distribution make housing expensive?

My guess is that they meant: If you give a lot of people that previously couldn't afford a house more money it will increase the demand and prices. The issue is that there is a shortage of housing which is primarily due to zoning preventing the construction of houses in a lot of areas.

Ah this implies definition of wealth is purely $ value, not what their inflation-adjusted “afford to buy material goods and services” value.

for any given dollar a middle class/poor household would be more likely to spend it on housing or additional square footage than a richer household

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