Problem with this analogy is that software development != revenue. The developers and IT are a cost center. So yea in a huge org one of the goals is to reduce costs (admin) spent on supporting a cost center.

Doctors generate revenue directly and it can all be traced, so even an extra 20 minutes out of their day doing admin stuff instead of one more patient or procedure is easily noticeable, and affects revenue directly.

You mean, there's a 1-1 correlation between the amount of pointless admin a doctor has to do and the number of patients he sees (and thus the revenue of the clinic). It should be visible on the spreadsheet. Whereas, there's not a 1-1 correlation between the pointless admin a software engineer has to do and the number of paying customers a company gets.

But then, why do large orgs try to "save costs" by having doctors do admin work? Somehow the wrong numbers get onto the spreadsheet. Size of the organization -- distance between the person looking at the spreadsheet and the reality of people doing the work -- likely plays a big part in that.