The US isn't heading toward "miracle treatments for the rich", it's heading towards "over testing, over diagnosis, and over treatment for the rich", all of which are linked to harm.
And single payer systems mostly don't prevent private treatment - you don't need it because the single payer is good quality and the only benefit you get from private treatment is access to ineffective experimental very expensive treatments and nicer hospital rooms.
And single payer systems mostly don't prevent private treatment - you don't need it because the single payer is good quality and the only benefit you get from private treatment is access to ineffective experimental very expensive treatments and nicer hospital rooms.