This is routinely overstated. Vacant rental units are abundant, particularly in higher income buildings. The vacancy rate in Houston, for instance is one unit in ten. High income units were twice as likely to bee vacant as their low cost peers, with 30k brand new units on schedule for delivery in 2024 concentrated inside 610.

This, in a city with around 3500 homeless people in a given year.

To claim we just don't have the unit space is denialist.

It's actually denialist to claim that the only facet of the housing crisis is homelessness. There are a myriad of other problems with housing that can only be solved by building public housing, especially around public transit, which we also need to build a shitload of.