We do, however, like the term PA.
Adding an apostrophe dramatically changes the meaning. For example:
The Surgeon General is the operational head of the US Public Health Service Commissioned Corps.
The Surgeon's General is a hypothetical TV show (probably on basic cable) about a military leader who does the laundry and other chores for a surgeon.
Physician assistants are a crucial part of America's health care system, practicing medicine and prescribing medication in all 50 states and the District of Columbia.