As other posters have pointed out, much of the sorting is based on pure practicalities. My own experience has been hiring for a large Wall Street law firm and a bulge bracket IB, and the considerations were the same for both firms. Whether we were hiring first year law year associates, analysts or IB associates, we were trying to find the most qualified employees for the positions to be filled. The primary qualities we looked for were intellectual horse power, communication and interpersonal skills, energy and work ethic. The time and resources we had for hiring was limited. The selectivity and quality of education of various colleges, law schools and B schools acted as an initial filter for us. It was more likely that we would find a greater number of top quality candidates at the top schools than other schools. We sent 2 interviewers to each of Stanford and Berkeley law schools to spend a full day there, and maybe 1 of us would spend half a day at Hastings after pre-screening resumes and transcripts. I am sure there were some more highly qualified candidates at Hastings that we never saw than some we saw at Stanford and Berkeley, but as a business you allocate your time and resources to higher probability opportunities. This same type of resource allocation was applied to B school recruiting and undergrad recruiting.
As we got further down the funnel, the institution mattered less and the individual qualifications mattered much more. Although I would say, all other things being equal, a top quartile student from YLS or Stanford BS would be viewed much differently than a top quartile student from UCLA or UT law or business schools. @Sherpa’s son captures the process pretty well.