Meh, there's caveats in this discussion that aren't totally transparent.
Where I did residency, there was no mandatory call after second year. Transferring to a program with call would have been extremely unappealing to me especially because who knows what that "easy" call schedule would actually be like. Otoh, if my residency had a bad PGY-4 call schedule, this could have been nice. Ymmv.
Transferring and being a chief could be a great opportunity if it's a "chief in name only" type of position. Ie, chief has very basic duties like making the call schedule. If it's a more in depth position requiring knowledge of the system, it could be terrible for the time they're a chief which might not be worth the prestige.
While being at an "affiliated" hospital can give name recognition in some situations, especially if the name of the home institution is in big letters on the diploma/certificate, the uninformed elites that prestige caters to often won't care. I actually had a conversation about this over the weekend with at a party who asked why they should pay more to see someone from a "second-rate affiliated hospital" instead of someone from the "real" institution. Didn't matter that the affiliated hospital was probably better for the area of care we were talking about, logic often disappears when prestige and narcissistic traits get involved and fallacies in thought are abound.
Geography also matters. I'm sure the name recognition for Beth Israel carries a lot of weight in the NE area, but in other areas of the country it won't. No one in the midwest outside of medicine knows anything about hospitals "affiliated" with Harvard. The names Beth Israel, or McLean, or Spaulding don't mean anything. Brigham and Women's Hospital or Boston's Children's Hospital will ring bells, but anything short of Man's Greatest Hospital won't mean much. Only the real giants like Harvard, Yale, Stanford, etc. will carry that kind of weight nationally to the general public.
To the point of fellowships, those elite people looking to spend money only want *the best*. "You didn't do a fellowship? Why bother seeing you? Oh you went to Harvard? Then why didn't you do a fellowship. Must not have been good enough. I'll find an expert." Never mind that this is often irrelevant to most of psychiatry and that even the *perceived* "elite" programs are obtainable to decent applicants. Tbf, those same elites would also scoff at a fellowship from a lesser program anyway, I saw them do it repeatedly on one of my rotations in med school.
Some elite academic programs may only want to hire from other elite programs, but many don't care. I've gotten e-mails for job listings from recruiters from Yale, Duke, Northwestern, and California schools as well as plenty of solid but not "elite" programs like Case Western, Montefiore, Wake Forest, and Boston University. Some are at the main programs/hospitals, some are at affiliates with residents rotating through. Go to some job fairs/booths and get on the right lists and one can find plenty of academic positions even straight out of residency. Truly breaking into the depths of academia in the heart of elite programs is obviously more difficult, but getting an affiliation to add to your CV? Not so much.
A transfer like this certainly could be beneficial depending on what someone's career goals were and if they want to stay in the northeast, if they need specific connections to open some doors, or if they just really dislike their current program. But it probably also wouldn't make a huge difference for the average PGY-4-to-be in terms of career trajectory.
