I'd define it by the meaning of the word. I don't get to choose a new definition then what it actually means. So in other words, the way you're defining it.
The idea that Hahn was loyal to those wrestlers is dumb. He was loyal to the team. That's why he asked the team. All of these coaches are loyal to the team and what's best for the team (in part because of how what's best for the team mostly lines up with what's best for them). The idea that a coach should be loyal to an individual wrestler over other individual wrestlers or to the team as a whole is dumb. Cael Sanderson owes loyalty to the PSU wrestling team. Not to every individual PSU wrestler in all situations. If he owed loyalty to every individual wrestler regardless of context, then he'd make it about 15 minutes before those individual loyalties would conflict. For example, he recruited Ryder with Jack Kelly on the roster. Nobody cared that he recruited a better wrestler over a worse wrestler. But now that's a big deal and it's disloyal because he owes the job to the guy who was brought in over someone else initially.
This sport is built on the best guy winning the spot. The idea that a coach is supposed to counteract that and keep better wrestlers off the team is dumb. It's hand wringing from fans who want to find ways to make big teams that they don't root for into bad guys.