I would have to politely disagree with your opinion on a coach letter of recommendation. If you are a collegiate athlete, I believe it is okay to have an extra letter of rec from a coach. My coach wrote an excellent letter commending me on leadership, commitment, work ethic etc. His letter was brought up in several interviews. When the adcoms brought up the recommendation letter, it also opened the door to discussing my experiences with being a D1 athlete and captain. I truly believe that it helped me stand out and I was subsequently accepted to all the schools I interviewed at.
Now, OF COURSE you wouldn't submit a collegiate coach's letter instead a Doctor/Research Leader/Professor letter. The letter from a coach would be a supplement to your application. For my application, I also submitted two vet letter of recs and two professor/research letter of recs. You obviously wouldn't ask your coach for a letter if you quit during your four years, were a bad teammate, or weren't a leader on your team. But assuming that you already have letters from Doctors/Professors and were a positive addition to your team, I believe it is safe to add a letter of recommendation from your coach.