Coaching, even up through college, is mostly about who is willing to grind it out. Few people want to toil making next to no money for years, not knowing if you'll get that opportunity to be a head coach in high school, or grab on to a minor role in college and then just network for a better gig, jumping across the region (or, more likely, the nation), unable to support yourself doing that one job. It's not about superior intellects (even within that sport) simply doing superior things ... those with great minds aren't passing on a career as an astrophysicist or neurosurgeon to coach. The townies who are hometown heroes (or want to be) are typically the coaches. Or, as you said, a teacher who just wants some extra easy money.
There's a reason mediocre quants are coming in to sports organizations as analysts/consultants and blowing up the traditional coaching/scouting structure in many sports ... because all these "life long experts" in the field don't know **** (or nearly as much as they think they do). That goes up through the pro ranks. And the "life long experts" actively fight against acquisition and application of knowledge. Imagine the awfulness that exists at the high school levels if the pros don't know their ****?
Hoops was my 3rd sport, but I was still a starter (barely) or 6th man. Being a 5'11" power forward with no hops, I had to use my noggin to succeed. Most of my teammates were mediocre intellects, at best. Some were dummies. I was the one having to tell them the tendencies of our opponents and all that fun stuff that helps you win games, outside of athleticism and skill. At least 5 of my teammates went on to become high school basketball coaches in some form, including some long-time successful head coaches still out there coaching ... and actually another became a D3 college coach. The best player (by far), who was smart, did well academically, and was a floor general on the court, never became a coach because, after he played in college, he went on to a successful career in finance. I never coached (any sport, except on a volunteer youth basis), because my career took me far away from that. I've had parents and current coaches ask me, based on my volunteer experience, if I'm an actual coach, and prodding me to either become a coach or set up private instruction ... but I just don't have the time nor the inclination. I just give them the information for free.
The only kid from my high school baseball squad, other than one kid who also became a hoops coach (he became a teacher at the same school), to become a baseball coach was a kid who seemed stoned all the time (wasn't the brightest bulb on the field, either), and who never made it past community college. He's been a successful Legion coach for decades. No one from my college team coaches, that I'm aware of.
In football, our head coach for a couple years was terrible. We underperformed greatly. We had a program that was typically successful, a lot of talent that went on to play in lower-level college (still well above average for our area), we were successful as a team in each step up until varsity, and we still had 1-win seasons at the varsity level with this guy at the helm. Just awful decisions in who was playing where, and the play-calling was mind-numbingly bad. He went on, shortly thereafter, to coach in college and has now worked his way up to being a D1 coordinator. One kid a class up from me in high school was constantly in trouble in school ... barely staying academically eligible to play, getting suspended for behavioral issues (including some legal stuff), and never even played because he wasn't very talented ... just a bad, dumb egg you wanted to stay away from. Last I knew, he was a top assistant football coach at a successful private school in my old stomping grounds.