Personally, I think the Order of Ikkos program USOPC has is better: When you win an Olympic medal, you can give an award to someone who you think has contributed to your success. It might be your primary coach, it might a strength coach, it might be a dietician. It's a nice way for athletes to acknowledge people who might not get recognition, and it doesn't just automatically go to the head coach of a program (who might end up getting a bunch of coach medals otherwise).
As to who is designated their "coach," at least at the Olympics, the athletes fill out forms and they decide who that person is. No one is fact checking that - if they want to list themselves or their high school coach or their strength coach or leave it blank, it's up to them.