I've been hearing people react to current (American) college admissions by saying the problem is the Common Application allowing people to apply to many schools at once.

I would be more likely to locate the problem in increasing numbers of applicants rather than increasing numbers of applications per applicant, but I wouldn't be opposed to seeing a more centralized system go up. American medical schools accept students through such a centralized system. Chinese university admissions isn't centralized to the same degree as American medical schools, but it's still quite centralized, and more formalized.