What you're claiming makes it sound like seeking graduate acceptance requires manipulation and only nepotism guarantees acceptance. Other people are not a means to an end but instead the ends themselves. I don't see anything wrong with a friendship with a faculty member, but you make it sound as though the right way to do things is to have an agenda for getting a faculty member's attention so that they might "put in a good word" with their faculty friend at some graduate department to grease the tracks of acceptance.

Certainly, relationships are important, but they're only valuable if they're genuine, a two-way street, and not one-sided. What possible incentive would a faculty member have to invalidly get an undergrad accepted to some grad program? Just because they like them? What do they get out of it? This all brushes very close to psychological egoism and narcissism.

Of the 20M or so undergrads at any one time, what percentage of them are doing graduate level work? Some... I took graduate seminars as an undergrad. It's not all that unusual, but whatever an undergrad does, even at MIT, is for the exercise, the experience of doing it, and not for pushing the state of the art and publishing articles. Even if an undergrad does publish in a journal, it is going to be clear the purpose of the exercise was the experience of doing that work, and not advancing the field. Undergrads think they know everything. Grad students know they know nothing. PhD's know everyone else knows nothing.