Basic income is not going to be able to provide housing in the absence of other programs; it will just end up captured as increased rents against a static supply of deteriorating housing stock.
This model of BI (replacing existing programs) is nothing but a giveaway to landlords, which I assume accounts for the PR juice behind it.
It's possible to have social housing that's not terrible or stigmatized. Having moved from the US to the Netherlands, the contrast is remarkable. Social housing here is integrated in most neighborhoods, not a "hood" of its own. There are definitely exceptions of course, but even the Schilderswijk or Bijlmermeer are very pleasant places compared to most NYCHA projects.
It's mostly just rent-regulated housing, be it owned by non-profit housing corporations, coupled in case of direst need with a subsidy payment, and with agencies responsible for placement. Not, actually, much different the administrative structures present in most American cities. The main difference appears to be first an explicit goal of avoiding segregation, and second, scale. Most rental housing here is in the social sector, so the benefits extend beyond the very poor, which is critical for avoiding stigma and maintaining political support.
Replacing landlord oversight with cash payments to tenants is not going to do anything to improve the lot of the tenants. I'd rather see the US invest directly in expanding affordable housing integrated with neighborhoods.
Unfortunately, this is a political loser until a majority of voters stand to benefit directly from it. Things are going to have to get a lot worse before that happens.