Admissions has a tricky job since there are many more outstanding students than they have slots for - even limiting to perfect test scores and grades (usually with top quality essays, recommendations, etc. as well.) Many applicants end up with the same admission ranking (and those rankings still have a large margin of error as you note). Selection becomes arbitrary, based on ancillary factors (hmm, how many concert pianists vs. cellists are we admitting? do we have too many prospective CS majors and too few history majors?) Which is why they argue that at the margin they can consider demographics (for example balancing the number of men and women), geographic origin, socioeconomic status, athletics, donor status, etc. Truly random would be fairer however.

The problem has worsened over decades; applications have ballooned ~7x (600% increase) since the 1970s, while class size has only increased by 15%.