How would you solve for this?

Track followup rate and other metrics that would let applicants filter/sort to appropriately prioritize "cylindrical filing cabinet" postings.

Create a site that people who applied to an employer can go to announce they have, and employees can look up the numbers themselves. It'll give employees a feel for application numbers, and those who are tasked with interviewing will have a feel for the actual rate of candidate generation.

Or, as a hiring manager, don't be a douche and be candid with your team.

I've just started using Otta for my search and they publish responsiveness scores. Not sure if it's by role or across the company. It's saved me from wasting time on companies with bad hiring practices (assuming scoring is accurate)