The flaw in your argument is the base assumption that profit is bad. Greed is bad, profit provides incentive to do it better and less expensively than the next person.
Your provider won’t approve a treatment that could save your life — can you switch to another provider? Of course not, YOU HAVE CANCER and you’ll never be approved
A red herring, in you only have the NHS, you can’t switch either, and courtesy of NICE, they don’t approve every treatment.
It would be very expensive here, but we are already spending the money via insurance premiums and taxes.
How will it improve the system? The core problem with the British and any other health system remains the spiralling demand for the services. Our obesity and diabetes epidemics aren’t going away becuase of universal health care.