The author is referencing an existing analogy from Fred Brooks, and building upon it.
Sure, today the anesthesiologist might be the most "important" person in the room, but that's not the idea behind the analogy.
Your emphasis that surgeons "heavily rely on the surgical team" is just as important to Brooks' beliefs, in that the "Chief Programmer" is only able to do what they do via the support of the team.
The "grunt work" (noted by the author) seems solely focused on tasks given to the "Co-pilots" (or assistant programmers), notably with no specific mention to the other supporting roles (admin, editor, secretaries, clerk, toolsmith, tester, and "language lawyer"), many of which have been replaced by SaaS tooling (Github, Jira, Notion, Docusaurus, etc.) or filled by other roles (PMs, SDET, etc.).
Furthermore, the author even states:
> I hate the idea of giving all the grunt work to some lower-status members of the team. Yes, junior members will often have more grunt work, but they should also be given many interesting tasks to help them grow.
The author clearly sees less experienced programmers as mentees, rather than just some grunts whose work is beneath them.
The analogy may not be perfect, but their message about "AI coding tools" should be valued without judgement (and without accusations of egocentric thinking).