A. Columbia does not track interest, and,
B, Columbia professors have little to nothing to do with admissions.
So there is no point in the entire exercise, except to cold contact a person and tell them that you really really really want to attend their university.
Since I have worked by now in half a dozen universities and am friends a colleagues with dozens of faculty, I’ll tell you that you are wrong.
While professors will be happy to make the time to meet with enthusiastic undergraduates and even high school students and speak about their research, advances in their fields, and even how a person ends up a colleges professor. They have little to no interest spending their time listening to some prestige-obsessed teenager go on about how they (the teenager) REALLY wants to attend the professor’s university.
Moreover, and this is important, a professor who spoke to a high school students is not likely to pick up a phone and tell admissions “Hey, you need to take this kid”. Even if they did pick up the phone, admissions would tell them to do their own job, and not to tell the AOs what they should do.
First, you son was contacting these people to obtain important information that he could not get from, say, admissions, and second, U Michigan does track interest, unlike Columbia. So this example is not really relevant.
Performing arts degrees are a VERY different kettle of fish than Columbia University. To begin with, the people who interview for performing arts programs are not AOs, but faculty. SO meeting with faculty is beneficial for admissions, and admissions are part of the job of Fine Arts faculty.
LACs are not Columbia University, and many LACs track interest. Moreover, LACs are pretty small, and professors do speak with AOs, and can “put in a good word” for an applicant.
If the OP was thinking of contacting a faculty member at Skidmore, I would say that the definitely should go ahead and do it.
Again, the point is that Columbia does not track interest, and “showing interest” does nothing to help an applicant’s case.
So this example is not relevant to the OP either.
You’re telling somebody that they should take use public transportation to go to work in Dallas, because the public transportation in Boston is a better option than driving.
PS. Contacting faculty just to learn about a college and to help you decide whether you want to attend can be a good idea, though I really like @DramaMama2021’s idea of having admissions connect you to a faculty member.