There are a limited number of seats available at each school. Admissions is essentially a zero-sum game. If, for example, Jose is a Hispanic Teach for America applicant, and he visits, makes a favorable impression, and is admitted, he has just taken up a slot that another Hispanic, non-traditional candidate will lose the opportunity to gain. Similar to political lobbying, it is likely not worthwhile for any individual competitor to invest in obstructing another candidate's lobbying activity, but aggregated lobbying activities significantly diminish the chances of everyone else.
Using the example, if a school targets 20 seats for Hispanic candidates, and
100 Hispanic candidates apply so baseline admission chance is 20%
However, 10 of these 100 Hispanic applicants visit
5 of these 10 applicants make a strong impression and are admitted
There are now 15 seats remaining for 90 non-visiting candidates. Their average admission chance just dropped to 16.6% They were hurt since they did not visit.
There are 2 questions:
The first question is, are MBA applications evaluated by the admissions committee in such a way that whether an applicant visits a school makes a difference in whether an applicant is interviewed or admitted? Does the school visit checkbox overtly affect application scoring?
If the answer is yes, then applications are clearly more complicated than face value, with the school visit another way for applicants to distinguish themselves. School visits would be another way for applicants to gain a competitive edge, like retaining the services of an admissions consultant.
The second question is, whether adcoms are sufficiently influenced by impressions made by visitors that they admit those who, had they not visited, would have been denied without an interview.
If the answer is yes, that would affect every other applicant's admission chance and be a game-changer, even if the first question's answer is no.
I think it's relevant that most strong(on paper) applicants would eventually visit to interview. All applicants invited to interview would have the opportunity to make their personal impression. The school visitor only makes an impression at an earlier stage of the game, whereas non-visitors may catch up when they visit to interview. As long as the answers to both above questions are No, then making an in-person visit to make an impression would have no effect on admission outcomes.