Is the government going to give them a car too? What good is a house to a person that has no transportation. How are they going to get to/from anywhere with how most neighborhoods are set up? There's nothing in walking distance for them. A better solution would be for the government to tax the shit out of residential property that the owner isn't living in so they're incentivized to sell. Then the people that are currently renting can buy, move out of their apartments in more walkable areas and free them up for whatever the government needs to do for the homeless.
Lots of homeless people have cars. Often, they live in them. That said, it would be better for them to get to work by walking, cycling, or using public transportation.
I think it's valid to address issues with proposed solutions, especially prior to their implementation. For what it's worth, their argument is not entirely sound, since most these proposals have built in subsidies for home buyers, but it's good that they are providing their perspective.
I mean, it's not just them in that situation, and it seems uncharitable to claim their only concern is self interest. I stand by my original point that it's important people speak up about how situations affect them, and I'm not sure I'd call that self interested. Since I don't know them personally, I'll give the benefit of the doubt. Housing as a right is a cornerstone of leftist ideology, so I want to make sure people feel comfortable talking about it openly and debating implementation and bringing up when people might be left behind.