AFTER EDIT: Important background information for this thread is that hundreds of colleges in the United States already have explicit policies of open admission, meaning that they admit all applicants, and the majority of colleges in the United States admit the majority of their applicants. Only a few hundred colleges (out of about three thousand in total) are selective by any meaningful definition of "selective."
It normally costs ~$50 to take the SAT once, plus ~$12 per college you want to apply to. Then there are the SAT subject tests, which cost less ($30?) but it's not uncommon for a student looking to get into a selective school to take >3 subject tests. Then, maybe the student needs to retake the SAT, which is pretty standard, so add another ~$50 dollars and now we're looking at several hundred dollars in exams. This isn't counting the $50-100 application fee per school. Having a professor interview applicants would still be impossibly expensive of course. Do you happen to know how well the alumni interviews work? I never had one, but if I understand correctly, they are a part of Ivy League tier applications where a graduate of the school deems if the applicant would be a good fit. I've heard there's not much weight placed on them, however.
I personally think the SATs are better indicators of socio-economic standing than scholastic aptitude, but agree that there's probably nothing better. I kind of wish that the application process was similar to that for graduate school, where there's more weight placed on the relevant subject test and letters of recommendation.
I cannot imagine how expensive it would be for an admission committee panel to meet with 10,000+ applicants (like a big state school gets every year)