In Canada, there really isn’t any such thing as “your own doctor.” There’s the doctor that the government sent out to practice medicine in a slightly larger town 40 miles away. Since the next closest one is 220 miles away, that one will have to do.
Death panels? When you’re seriously ill and you’re on a waiting list two years long, doesn’t that resemble a death panel?
Not true. There is a shortage of doctors in smaller towns but in any decent-sized city there are plenty of options.
Access to doctors in rural areas is problematic sometimes. Many doctors do not want to practice in rural areas. You absolutely can choose your own doctor. I have had the same GP (my choice) for 40 years.
I'm not sure where you are getting your information.