You're missing the single best part of it: add on top of that mentorship from someone who's a world-class expert. My PhD advisor was probably the single best programmer I knew.

He taught me things about the Linux kernel that I'm not sure I could have learned anywhere else. I'm sure plenty of programmers are kernel experts, but none of them have the time to sit down and do an all-nighter hackathon with me the way my advisor did.