At our school we do not have coaches in our administration (just the rest of Alabama). Our director has a masters degree in math (not math ed) and the three vice principles, who also teach, each hold a Phd. (English,Physics, and Film Criticism).
As for the shortage in math or science teachers in Texas or anywhere else, this situation is always artificial. I've got a crate full of resumes in my office of people with advanced degrees in math who are looking for a job. My advice is to drop the moronic certification process and boot out the educrats!!
I, myself, am a lifetime athelete and former varsity tennis player. There is nothing inheretly wrong with being a coach-- I wish I could do some coaching. I just believe that young people need to be surrounded by educated adults when they are in school!!