That's true, but if it only covers the lowest cost of living, then...it's not enough.

Basic income would probably affect costs of living to some degree. But if you still need a job to live somewhere then you still have to bow and grovel and let that employer own you unless you can save enough to be sure you can relocate.

There's probably a number of ways to resolve this I can't think of right now.

Basic income might not mean you can live anywhere you like, but it fails if anyone on it is unhoused.

(Note that I don't count the people who might choose to eschew traditional housing here. The old couple who live in their camper so they can travel everywhere before they become too disabled are not unhoused, for example).