I agree with this mostly, but to be honest, since there are so few neuro-psych programs (and probably with good reason), I'd just forego applying to the individual psych or neuro program at that single institution.
I don't know how it works everywhere, but for combined programs I'm familiar with, the interviews aren't entirely separate. Like, for triple board, you might spend a day at peds and a day with the psych folks for the interview. Folks would usually declare "yes, I want to do triple board, but if I can't get a triple board slot, I'd like to match in peds" or "psych". Usually the program would then rank them in the triple board match, but then also rank them in the categorical peds or psych as well just in case they don't match triple board, because there are so few combined slots, and the desirable ones are more competitive.
I don't know if that's how it works everywhere, but that's how I believe at least triple board works in the programs where I know people (Brown, Pitt, Cincy, Kentucky).
Triple board is essentially a "child psychiatry plus" program for the most part, and I don't understand people who want to be pediatricians if they can't do triple board.
FM/Psych works much better if the person sees themselves as "FM plus", so I agree they should screen out for psychiatrists who don't want to hang up a stethoscope. That doesn't mean someone won't wind up practicing more as a psychiatrist, but the programs generally (not always) work better if the primary identity initially is FM who wants more psych training.
I know little of IM/Psych except that it seems quite a bit different than FM/Psych.
And neuro/psych, I have no clue. I could imagine it going either way. I know a few attendings who have completed both trainings independently, and one works mostly as a neurologist, and the other as a geriatric psychiatrist. The former was annoying because he would cover neuro on the weekends at a community hospital we cover, and he would recommend that many of the people he saw get a psych consult, sometimes for no good reason, making lots of unnecessary work for us. What we could do in an hour that he couldn't have done with an extra five minutes was always beyond us. To be (un)fair, 5 minutes of an attending's time is probably worth more financially to an institution than an hour of of a resident's time.