The question: Should coaches be hired solely on the fact that they are also teachers?
Avery Thrush - No!
Nothing is worse than an incompetent coach. Hiring someone simply because they have their teaching certificate - and not necessarily their coaching license (which is arguably more important) - is only hurting the program, athletes, and reputions. Meanwhile, athletes are missing out on a coach who coaches simply for the love (and knowledge) of the sport and NOT the added pay.
Sports such as track, swimming, and cross country usually suffer the most from this system. These sports are typically thought of as needing less technique and more strength training: therefore, they attract more inexpirienced coaches who think all they need to do is have the students run endless laps to get better. This is not true. These sports require just as much sport-specific technique as football and basketball. You have to know the muscles affected, the stretches needed to target those muscles, the drills to develop your technique, the workouts that are appropriate for a specific part of the season... all things that a typical teacher cannot provide. This knowledge can typically only come from a veteran of the sport.
Choosing coaches based on their teaching expirience can also affect the quality of education that reaches the students. Aspiring coaches in the US often do they only thing they can to be able to coach high school sports: get their teaching certifcate. This practice only devalues the educational system and hurts the students. It nearly certifies that the teacher's heart will not be fully in their teaching. Their coaching excellence will be crippled by their incompetence in the classroom. Finess on the field will translate into failure in the classroom.