I think someone could self study and become a lawyer or banker / stock broker, but licensing requirements would prevent it (not necessarily for good reason).
In some states, California being one, you can "read law" while working for a member of the bar and then sit for the bar exam. The CA bar exam has 45% pass rate though, with most takers having gone to a good law school. YMMV indeed.
Disagree about banking (having gone to business school and worked on Wall Street myself), but would add doctor/nurse, engineer, psychologist, and most other jobs that will survive the automation apocalypse.
Unlikely, expert systems outperform doctors at diagnosis already. Nursing, perhaps not yet. There are supposed to be exams not requiring education, but internship is still a prerequisite and hard to get.
Engineering is mostly mathematics and physics. Doable by machines. You probably meant design instead.
Psychologist, well, first they have to actually be good at it...