I certainly agree that there are people who teach because they can't do, but I don't think that teaching because you can't do is even part of the kernel of teaching.
As for admins... this is a huge problem right now. They are threatening to destroy the host. But a healthy host does have a trim, effective, and dedicated group of admins.
If you’ve been out of school for >10yrs, I’d strongly encourage you to look at the current cost of your alma matter - it may well shock you.
Clearly there are lots of people who genuinely choose to enter teaching, but in certain subjects, for some people, it is the de-facto profession if you cannot use your degree to do something else. See Avenue Q's "What can you do, with a BA in English?".
This is more about high school than university-level though.
[Note - I was mistaken - please see the clarification in post below!]
Lol I think you’ve got that backwards!
The marketing slogan was a play on the common criticism of teachers which is a quote of Shaw from around 1900.