By far the most difficult jobs to hire for are your Olympic sports. In my time as an athletic admin the hiring process for sports like XC, Swimming, Golf, Track, Tennis come down to simply can they pass the background check as you mentioned. And don't even get me started on middle school athletics. If you can find a young, ambitious middle school coach who wants to be involved in multiple sports you get them in your office asap and start signing HR documents immediately.
Football, basketball and baseball are a dime a dozen when it comes to resumes. Those positions you actually have to / get to conduct real interviews where you discuss philosophy, strategy, long term goals, weight room, etc....
Parents would be surprised to learn that when we hire a person and they're like how'd they get hired, well it's because maybe they were the only resume.....literally in many cases.
We're also seeing fewer and fewer teachers who want to tackle the job of teaching and coaching.
I've said on here multiple times in the last 3 years that we're seeing the beginning of the end of what high school sports use to be. I stick by my 10 year forecast (well now 7 year forecast) that high school sports in the USA will look more like what goes on in Europe or Japan with no scholastic affiliation, just club status.