Any teacher or coach who says doesn't have favorites is lying.

It's human nature. For what is worth, I never believed Alina became Eteri's favorite. Not because she doesn't do favoritism but not that year. Evgenia was always her "pet". She should have asked Julia for confirmation, if she was in doubt.
Anyway, the problem is not having a "favorite". The problem is when your teacher/coach doesn't dedicate the time needed for you, or doesn't give the right material. I don't know the internal dynamics but I doubt Moskvina is lacking in professionality. She has had top level teams who were rivals before. B&K had two very good programs and they have so much talent. I think someone like Moskvina can see that. Again, I don't know if there serious issues in their camp. But if they need exclusivity, then perhaps it is better to change. Whatever they need to do they should. But in the end it's up to them when it comes to competition. They have to deliver, not the coach.
I guess we'll have to wait and see. I'm curious what they will bring up. By the way, who is Filipp? Any relationship with Tarasova?