This is mainly a problem with schools perceived to be “top 30.”
Kids with perfect stats and strong ECs get routinely rejected from these schools because something in the holistic assessment meant that someone else got the slot. Maybe someone else’s essay resonated more with the regional AO, or someone else filled a demographic box the university was trying to fill.
Kids aren’t stupid. Applying to dozens of schools is simple game theory to maximize your odds of getting in to a top program when decisions seem semi-random. There are tons of examples of kids rejected at 7 other top schools who got in to Harvard.
If your admissions dept is overwhelmed, then hire more admissions officers. It’s a good problem to have.