I think the hard part/area of concern is the hiring market. Do those doing the hiring know which are the strong programs and which aren't? Are they going to grant you admission and/or OB privileges because you went to a strong program, or are they going to push you into the limited scope of the lowest common denominator? Also, are patients as likely to choose an FM doc over an internal medicine doc if the specialty is diluted by crappy programs? (Similar things already happening to an even worse extent with NPs, where degree mill crappy programs are pumping out FNPs and damaging the reputation of all NPs, even those with years of experience in nursing pre-NP and who attended high-quality graduate programs). I dunno that it is as easy as saying "strong programs will stay strong" unless you can take that strong training and earn a living still practicing to the full scope under which you were trained.
So what you're describing is not how the hiring/credentialing process usually goes.
People who are responsible for hiring generally don't know if you went to a strong program or not. This is particularly true in IM/FM/peds, where there are soooooooo many programs. They may only know about the programs in their immediate geographic area, but I wouldn't even bet on that.
Hiring usually happens by word of mouth. "Dr. Smith, who has worked here for 10 years, said that his buddy was looking for a job and suggested that we look at his CV." "Dr. Jones is from Generic Hospital Residency Program; we've hired 12 of their grads over the past several years and they've all been good, so she's probably fine too." "Dr. Doe said that the applicant was her intern when she was chief; she vouched for this person." "His current CEO called our CEO, and asked if we would hire him." But the "strength" of your program is almost never a factor.
Credentialing, or the process by which the hospital/clinic approves you to perform certain procedures, also has nothing to do with the reputation of your residency program. For a minor office procedure, they may watch you as you perform a few of them. Once they're satisfied that you know what you're doing, they'll sign off on it.
For anything more significant (like intubation or vaginal delivery), they will require case logs from your residency experience, as well as directly observing you. So it's up to you to keep good records from your residency experience, if you think that that procedure is something that you will want to do as an attending.
Also, are patients as likely to choose an FM doc over an internal medicine doc if the specialty is diluted by crappy programs?
VERY very very few patients know, or care, what the difference is between FM and IM.
98% of patients will choose you for reasons that have absolutely nothing to do with your educational background. "My roommate said that you were nice." "My wife saw you and said that I should come see you too." "My cardiologist said that you were good." "Your office was two blocks from my job and you happened to have an opening during my lunch break." "I liked the tie that you were wearing in your website photo."
The other 2% will choose you for reasons related to your educational background but not the reasons that you would assume. "I saw that you went to Michigan for undergrad. I did too!!! GO BLUE!!!!!" "You went to college in Georgia; I'm from there so I decided to see you." I live in Florida; a patient once told me that he decided to see me because he felt that anyone who had gone to school in Florida "has to be an idi**" and I had gone to medical school in Pennsylvania. I didn't agree with that assessment, but whatever.
What will probably happen with the new requirements is that programs that weren't strong in those areas will just continue to be weak in those areas, and applicants who are interested in those areas won't apply. That's all.