...The developers are paid by a lot of different universities and companies, and some are not paid by anyone (e.g. students)...
All "Bitcoin Core" developers are paid and "some [
contributors]are not paid by anyone". As I said, this is a significant distinction.
Most people need a day job to pay their bills, yes.
... Noone get paid by a company called "Bitcoin Core"...
By that logic, the U.S. Marine Corps don't exist, because all Marines are paid by the U.S. Dept. of the Navy.
Those are paid by a single employer to do a very specific job, commanded by one commander in chief. Try again.