After 4 years and maybe some moonlighting, you have hopefully built connections, know who to relatively trust, know where/what the good local jobs are, know where the demand is highest if you want to start a private practice, know the state laws to be ready for inpatient/forensic roles, maybe moonlight at a place that wants to keep you while you build a private practice, know who to avoid, have maybe built referral sources, know the real estate market for private practice, etc.
Also at this level, a MD after your name is already prestigious. In years of private practice, I’ve had 2 patients ask about my training and both seemed satisfied with the local name.
The average person is not going to know which programs are prestigious and which aren’t. In my area, Stanford, Harvard, and Yale are probably known by most as prestigious schools outside of Texas. The initials MGH means nothing with non-physicians in my area. I’ve talked to educated people that were surprised that UPenn is a well-regarded Ivy and not the community college to Penn State, believe UCLA (and most of Cali) is a bunch of crazy hippies, Dartmouth is a made up name, and anything with a Big10 affiliation is not prestigious because who would choose to be in the Midwest. Physicians have likely meticulously researched the best undergrad to get to medical school, interviewed and researched the best medical schools, and now spend time on SDN to better understand the better psych training programs that may lean toward different therapy trainings. It seems like more common knowledge to us because we have lived this game for years, but the average person applied to a random few colleges, went wherever they felt happy during 1 tour, or attended whatever school was the cheapest/provided scholarships. A recommendation from a trusted source goes much further than the name on your degree when it comes to someone choosing a doctor.
I would recommend going to somewhere that emphasizes training. If your preferred location only has a terrible training program, id rethink my local recommendation. Being a top 25 training program is not required to be a good training program either.