This - since you can live in a rural area with UBI - and you get more time in the day to manage your accommodations, the move to urban housing is not so critical.

Yes if you simply assert an upside down reality, this is a good solution.

However, people actually move toward higher COL areas as their income permits them to.

If more income meant people moved away from high COL areas, cities wouldn't exist. We'd have a flat distribution of people across approximately all land with ultra-low COL and ultra-low productivity everywhere.

You make a logical error here: you are supposing I'm referring to the case of someone moving to a place in order to earn more. I am not. I am referring to the case of when people earn more, they end up choosing to live in more expensive places. Both scenarios are true, but only one is the one I'm pointing to because it's economically identical to UBI.

No, I am not interested in the motivation at all, and it plays no role. That is the logical error you make. You are trying to make an argument based on current data, but that current data does not include the fact that income is correlated to location, but UBI is not. So your current data is not a proof of anything, really.

In general I agree with your view though that UBI could be captured by landlords, and that landlords are a special case. So let's introduce special laws for that along with UBI. Problem solved.

Alternatively though, if that turns out to be too complicated with too many side effects, I think there is a good chance that UBI leads to people being able to spread out more evenly, away from expensive and dense cities. You tried to make an argument why this will not happen, but as explained, your argument is not conclusive.