1000% agree with your comments. Soft skills are so important and I and my wife agree that ideally we want him to apply (and admitted) to schools that help him improve his soft skills. Find schools where professors really care about the students instead of treating students as just numbers, or teaching as "side jobs" because they care more about research, etc.
Your son is well on the right path if you all are already being intentional about finding schools that hone this. The material is the material, but improvement in learning and soft skills differs. Just my experience, but if many of the students articulate well the value that school has added to their ability to think and other soft skills, that is a good sign. They've been forced to think about it intentionally as well
One reason why those brand names you mentioned can be worth it is because the brand of those schools can make up for a lack of soft (and other) skills. But that only gets you in the door.
You said he wants a large school?
In my opinion, the floor is generally higher at a smaller school in which getting the students to their next step is priority #1 of the professors. They need your son to do well post-grad when there are so few in the graduating class. They have more of an incentive to be proactive in helping your son get to med school in my opinion, whereas that can be the career placement department's problem at a large school, but not always. The ceiling may be higher at a larger school- more people, more possible connections, bigger research, and a bigger test of soft skills. And you can find the same small school environment at larger schools depending on department/major.