Health insurance
A majority of US health care is paid for by government (it is slightly over 50%) versus being paid for by private sources. But there are other things to consider. Federal and State regulations require that insurance cover procedures that may not want to be covered. Insurers, Health care providers, and employers are required to fill out mountains of paperwork, and to store it all away.
Back before government got into health care, doctors hired 1 nurse for their office. That nurse not only was trained in her practice, but she also did billing and administrative duties. Nowadays, doctor offices have to hire a billing specialist, an insurance specialist, and at least one person to answer the phone and take appointments. This is on top of a nurse they may hire. If a doctors office must hire all of those extra people, the doctor will pass those expenses on to their patients.
Until Medicare was introduced, there were free hospitals. Most hospitals with religious names probably offered free health care to those who could not afford it. Under Medicare and Medicaid rules, the cheapest rates a healthcare provider can charge have to be charged to Medicare & Medicaid. That means if you offer free health care to one person, you have to offer it to Medicare/Medicaid.
Before government got into the health care business, health care was much more affordable.