The problem it can’t solve is that rich people might have to interact with mere humans.

I can relate. We, in Indonesia, have a problem where politicians, whose never even ride a train before, gets to decide the policies about public transport, and those who gets the consequenece is low-middle class who uses public transport. There was a meme from a year ago where a tone-deaf politician says the overcrowded trains in Jakarta doesn't exist even though it overcrowding is clearly a problem in regional line (KRL) due to lack of trains.

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.

Assuming we're talking about short distance trains, absolutely no, lol. It's just space inefficient. I will understand if it is a long distance trains, and it is a thing.