Poor people already have to live somewhere. It just paid for with rental subsidies and low income housing now, both of which also drive up rents for others.

Similarly, the US government already buys up milk to create a price floor, giving the milk away to the poor and to school lunch providers.

Housing would be a problem where supply is constrained, I can't see it being a big issue in the US.

I don’t buy that it’s a necessary consequence.

Even In your example if demand for houses goes down and demand for milk goes up, what prevents more land being used for dairy farming, more builders becoming farmers?