Let's say I agree with this idea and let's also ignore the fact that by stating it's a right, we are implicitly stating that someone else needs to pay for it with their own money if you cannot.
If housing is a right, does that necessarily mean that housing in a specific area is a right? I mean, I'd love a beachfront property in Maui but we can't all have that.
If we build a few million houses in the middle of Kansas and tell people "there is your free house, as is your right", is that enough? Or do people have a right to a free house somewhere just because someone in their family happened to be lucky enough to live in the same general area at some point in the past?
People in the US are generally allowed to move where they want. If a place becomes too expensive for them to live there, it's possible for them to move elsewhere if they must. I can definitely see that offering help with relocation could be good for society, and I can also see that having a mix of different people in an area is also good for society, but ultimately I don't agree that just because someone happened to pay rent at some point in the past, they and their descendants should be granted a perpetual right to stay in that proximate location forever.