Not sure that's a major issue for current customers; I saw a guy careening through my office parking lot at road speed just yesterday. No hands on wheel, staring at his phone.
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)
Many companies still have tons of job openings right after the day of their layoffs. You could argue they might be hiring different positions, but it's somewhat odd.
I think the Conventional PR Wisdom is that releasing a statement when you do things like this will be better than not doing it. So yes, most companies would make some sized press release and have a statement ready to go before doing something like this.