A lot of those ‘administration jobs’ are relatively new, and when speaking about private insurance a lot of them mostly involve interfering with doctor patient relationships. One of the issues with our current health care system in the US is that there’s been an explosion in the number of administration staff, but not much growth in the amount of doctors. https://images.app.goo.gl/Fyi6Vjc7H2Zq8hgq6

In the US we also pay the most of any developed nation for healthcare while generally receiving worse outcomes. Insurance companies spend lots of the money you give them trying to deny you care. Personally, when I needed to start chemotherapy for late stage cancer my insurance company decided to delay it by repeatedly denying the pre authorization I needed. My oncologist spent more time on the phone with insurance staff (who had no formal medical training) trying to explain why I needed to start ASAP than they did with me as a patient.

While most of those administrators might lose their jobs if we switch to a public healthcare system, a public health system also opens up other employment opportunities and non insurance based administrative positions. I also think any job losses are greatly outweighed by the benefits to doctors and patients, who rather than having to spend time/money/energy/resources dealing with insurance companies could devote all of that to better patient outcomes.