Most of your "evidence" has to do with kids moving between foster homes, or families running out in the middle of the night because they don't have money to make rent.

That is nothing like what we are discussing here.

The original OP is an anecdote. Could you link the extraordinary data? I want to see how they can empirically test this

At the same time I doubt anyone would use that kind of thing as evidence for forcibly settling nomadic cultures. I'm somewhat curious because I'm sure they try to do things like divorce socioeconomic factors, abuse, poverty, and other negatives from such a conclusion. But as someone who moved 7 times through 7th grade and attended at least 6 different schools through that interval, I'm generally quite grateful to not have been dulled and stultified by living in one place my whole life. To the point that I've contemplated planning at least one or two significant moves so my own children don't end up excessively influenced by whatever locality specific tints and delusions color a place. (Maybe another way to put it is its easier to boil frogs that have always lived in the same pot.) But I also do think it's nice for kids to have a solid friend group for a good part of childhood, and so forth. I suspect there's got to be a lot more complexity to this. (And I will say I do think there's a connection between moving a lot and loneliness, but I view loneliness as distinct from generalized depression. But totally not scientific.)