Seems like there's a twist of the words you doesn't do for the first time actually. In this case you used the word "monopoly" originally, now you changed it to "dominance". Those two words have pretty different meaning and I truly don't think I need to humiliate anyone to explain the difference. Let's speak about Eteri's dominance, which is coming from the reasons I mentioned above and somehow I see your words "there is something wrong with that" as the root of all problems. You obviously see the fact that Eteri is more succesful than other coaching teams as a problem. Well, that's a competition. It's like saying "this company produces better cars, but there is something wrong if they have better sales because of that."
If Eteri has a "dominance", it's not because she has a "monopoly" (because of any alleged rule that would force anyone to put their kids to her, again, see above), but because she is a better coach than the others and that is not something to be ashamed of but the other way around.