Not a necessary qualification for the job, but why wouldn't you choose someone who has demonstrated "more"?

Because then you're excluding economic opportunity from people who don't have that "more," even though the "more" is utterly unrelated to the job skill. Only people who have the socio-cultural background and access to financial resources that allow getting a college degree are able to get that "more." It's exclusionary and unnecessary and hoards participation in the economy to a specific type of person. It's like requiring a job candidate to be able to read and write in Latin, back in the day - utterly unnecessary, but it made sure that only a certain class of people got that job.

All that's left after that is brain jobs. At least for a while, until remote working takes those also. And brain jobs usually require some specialized education.

No, they don't. To be sure, a certain number of "brain jobs" do - like you said, a lawyer or an engineer. But most "brain jobs" don't require specialized education. Most of them have traditionally been held by people without college degrees. In 1980, only 17% of the population had graduated from college. That was the point of the study - there were millions of jobs that were being held back only for people who had college degrees, even though their current holders didn't have a college degree. It's just not true that there are only two types of jobs in a modern economy - those that require a college education and those that are purely muscle jobs.