Isn’t the fact that the current system is so extremely complicated (and because of that, expensive) exactly one of the reasons UBI is so appealing? Cutting out the bureaucracy will save a lot of money that can then be send to the people. If you spend $1000 to figure out that one person “deserves” $800 instead of $1000 you are wasting a lot of money/time for zero gain.

The people in the high rent area can move to a low rent area if they can’t hold a job: they have nothing holding them there under the UBI rules. As for kids, perhaps they should also receive (smaller) UBI that would go to their parents.