I don't think any parent or skater wants to switch coach often. Learning figure skating as a sport is not an easy thing. When a little girl started skating, probably eather herself nor her parents know who can teaching her to the top level. Mostly they'll choose a nice lady who can just stroke on the ice to teach. After many years of skating, they could finally understand it. Meanwhile they might have been through few lower level coaches who can just teach the girl very basic. On the other hand, for parents who have skated seriously themselves, or they have older children skated competitively, changing coach often might be their problem.