The problem it can't solve is that rich people might have to interact with mere humans. The car in a tube seats four and locks, so there's zero chance you'll have to sit next to a minority.
I wonder if rail would be more appealing to them if the coaches were designed as multiple isolated cells that seated 4-6, rather than straight-through corridors that permit mingling. (I've seen some old designs like that, in German narrow-gauge form)