This is factually false for anyone who has access to a lot of money. Such people have access to much better care and would likely lose it in a single payer system. See: UK, canada
Why do you think people come to USA for the best care when money is no object? Because the profit motive drives the existence of said care.
Routine can be done anywhere, and people go "anywhere". Fine. Specialty is mainly best in USA [1][2][3][...many more...]. So let's not ruin it, maybe?
[1] https://www.beckershospitalreview.com/oncology/worlds-top-on...
[2] https://health.usnews.com/best-hospitals/pediatric-rankings/...
[3] https://www.magazine.medicaltourism.com/article/best-countri...
[1] https://www.beckershospitalreview.com/oncology/worlds-top-on...
[2] https://health.usnews.com/best-hospitals/pediatric-rankings/...
[3] https://www.magazine.medicaltourism.com/article/best-countri...
And so on...
no they wouldn't, they'd still see private doctors in private hospitals, which is what rich people currently do in the uk as well.
they just might get taxed more for other people's health care.