The paper is conditional on starting grad school, though, which should remove a lot of these early selection effects. Of course, people could do a PhD for reasons different from obtaining a professor job. But they also show that people do get tenure, just at less prestigious institutions.

Yes. We also are not comparing to ppl with PhD parents precisely to avoid the “following parents” question. We compare to ppl with parent with a non PhD graduate degree (lawyers, doctors, MBAs, teachers mostly)