Personally, I think a coach with gymnastics experience of their own is the best. They know what it means to tumble on the hard floor and know from personal experience that it's good to do tumbling into the pit, tumble track, and mats as well, they know how to use equipment, they know the side of the gymnast, and when they say something like they know it's scary, or something is hard or something is easy, you know they are basing that on their own experience and aren't just saying it off of some book they read or some clinic they went to.
I don't think gymnastics clinics, and just teaching experience can fill in all the spaces that gymnastics experience does as a background as well. Of course it doesn't mean that just because someone has an elite gymnastics background then they are a good coach.
What do you guys think?