Just musing here about the effects of a lottery not on the pool of applicants, but the matriculants as well. The OP's link seems to be more about the rejected students that the accepted ones so I'm mulling while I eat lunch.
I wonder how those in the matriculating class, not just those who applied and were rejected, might feel?
Lucky? Not like they were the best of the best? Right now perhaps they feel they had an edge over other applicants, and who could blame them after all the hoops they jumped through? I guess it would depend on the personality of the student. Perhaps some would feel humble, others guilty, others deserving despite the randomness.
Knowing myself, if I were selected through a lottery, I would feel guilty and wonder if someone more "deserving" lost out. Of course that happens with the process now as well, but the students who are accepted may take some comfort in feeling it was a competitive process and not a random one. Explicitly removing that comfort could have some interesting effects.