I am seeing this question in a number of guises in the coaching blogs I follow. It seems to be an interesting question, but I don’t think it really is.
The skill sets of athletes and coaches are quite different. The primary difference is the athlete’s point of view is from the inside out and the coach’s point of view is from the outside in. This is why a collaboration between athlete and coach is so desirable. A collaboration joins the two viewpoints in the team, thus covering all of the bases (for want of a better sports metaphor).
There are a number of points which are subordinate but not negligible.
Coaches who were elite archers have credibility in their student’s eyes as someone who did what they want to do. You can’t buy that or train it in.
Coaches who were accomplished athletes and then train hard to become a good coach have both perspectives to call upon in their thinking. I, for example, was never an elite archer and think I am a better coach than I was an archer. (Although, the easiest person to delude is our self.) There are examples galore of athletes who were marginal at best in their accomplishments, but became quite good coaches. many ascribe this to the characteristic that marginal athletes are always looking for an edge and so learn more as they go, but I haven’t seen that proven.
I think people who think, “Well, they are a champion archer, I am going to get them to coach me,” are deluding themselves. Before picking a coach, look at their trainings, their coaching successes, and by all means, talk to them about their approach. If you have a lofty goal that this person can give you firshand perspectives on, by all means hire them for that purpose, but being a day to day coach is quite a different thing.
I have two documents I send out a lot: one is my Archery CV which lists my accomplishments and coach trainings, etc., the other is my coaching philosophy, stated as clearly as I can. If they are still interested after perusing these two documents we can talk logistics.