At this point we might as well adopt that joke where you blindly throw away half the resumes because you don't want to hire unlucky people.

At one point in the past a major UK a medical school adopted random selection for qualified candidates (Barts and The London School of Medicine and Dentistry - part of Queen Mary University of London). The approach benefitted qualified students from less well-off backgrounds vs those who can afford to win at the ever more elaborate (manual at the time) hurdles of resume assessment criteria and effectively game the system. There was an orchestrated campaign against the lottery around "Why gamble with would-be doctors?". Random selection was quietly dropped.

May be LLM resume screening is a symptom of a bigger problem - with tens of candidates per vacancy employers can screen resume badly and even throw half of the resumes away and still hire someone qualified.

A person's total luck is constant over a lifetime. The remaining half of the candidates already spent some of their luck in this selection, so they'll be on average less lucky than the discarded half.

Or more to the point. There are generally far more qualified applicants than job roles. That is training and education greatly expanded over the last couple of decades to produce more and more job seekers, whilst job creation hasn't really kept pace.

This hurts more than it should.