It’s important to remember, the plan for universal healthcare predates the current American system:

With the Great Depression, more and more people could not afford medical services. In 1933, Franklin D. Roosevelt asked Isidore Falk and Edgar Sydenstricter to help draft provisions to Roosevelt’s pending Social Security legislation to include publicly funded health care programs. These reforms were attacked by the American Medical Association as well as state and local affiliates of the AMA as “compulsory health insurance.” Roosevelt ended up removing the health care provisions from the bill in 1935. Fear of organized medicine’s opposition to universal health care became standard for decades after the 1930s.[14]

During this time, individual hospitals began offering their own insurance programs, the first of which became Blue Cross.[15] Groups of hospitals as well as physician groups (i.e. Blue Shield) soon began selling group health insurance policies to employers, who then offered them to their employees and collected premiums. In the 1940s Congress passed legislation that supported the new third-party insurers.

https://en.wikipedia.org/wiki/History_of_health_care_reform_in_the_United_States#1930s–1950s