> can afford to move

Basic income is precisely about "afford" part.

Those who won't move will benefit too because landlords will have to work on retention.

> Basic income is precisely about "afford" part.

This assumes that basic income either includes an allowance for moving or contains enough of a surplus over basic needs that savings can be accumulated.

I actually think that communities might sponsor your moving on their turf as this will mean you'll spend your BI there for prolonged time.