If anything, the administrators should go down in that time period that just happens to coincide with the mass adoption of computers by all businesses. What this graph is saying is that while the US population grew about 50% in that time (203-308 million), administrator incompetence grew 2300% over that time despite the mass adoption of computers. In other words, one administrator from the 70's could easily replace dozens if not hundreds of administrators today and get the same amount of work done. This kind of incompetence is beyond comprehension both at the administrator level and the executive level that hires them.

What do these administrators do (i.e. what's their value)? Are they like physicians with a leading/management role?

They apply "MBA 101" to the system, best summarized as "extracting more money with better care as a distant second".

Was chatting with the doc during our second birth, the admins had just pulled a bait and switch on the practitioners. Instead of better equipment and surgery rooms, they were getting a few hundred more beds. Beds are easy to bill for. Surgery and actual care are way less profitable.

I like how everyone forgets about this particular issue when talking about healthcare

Ignoring the elephant in the room is a traditional component of discussing healthcare in America.

Wow! I bet plot looks the same for the costs of higher education!!