Also, Yu-Na is the top female skater in the world right now, has broken all kinds of records, etc. Naturally, Brian is going to be attributed with some of that success, even though he might not have improved Yu-Na's skating that dramatically.
I will say, though; Yu-Na seems so much more confident since she's been with Brian. I think he has given her a sense of security. Plus, he seems like a very invested coach, too, what with his antics by the boards, etc. I guess that's why most regard him as a coach all troubled skaters should go to.
In regards to Caroline's coaching change, Brian's irrelevant anyways - there's no way he'll end up being her coach. Although Caroline could teach Yu-Na a thing or two about extension, and Yu-Na, well, there's a whole lot she could teach Caroline, too...