There seems to be a lot of misinformation in this thread...
Mishin does NOT shut off his students from outside choreographers. In fact, Liza's much-maligned long program this year was by - gasp! - Jeff Buttle (as was Artur's short). Liza also chose the Latin theme. She likes them. He does NOT restrict them artistically - the selection of Anna Karenina, for example, was made by Artur himself, not by Mishin or anyone else.
Liza's problems are physical issues related to the onset of puberty. Artur's are predominantly psychological (with a few physical thrown in). No coach in the world can just magically wave a wand and fix either problem. Ever. Mishin is handling them very well, I think, with support and a gentle grace that other coaches would not manage. I mean, can you imagine, say, Tom Zakrasjek being so gentle with a skater whose body changed so radically as Liza's? Or with a skater who suffered such severe psychological problems as Artur's? I certainly can't - he'd likely have broken Liza already and tossed Artur on the scrapheap.
A coach change is not a magical antidote to every problem. Sometimes it only makes the problem worse. Look at Abbott - all those coaching changes and no-one has ever managed to fix HIS head.
What I think would benefit Artur most, would be to keep this season's programs again next year. They are very nice programs, especially the beautiful LP, and if he didn't have to worry about learning new programs, it might help him to sort through his problems with other things. (Okay, and the selfish fan-part of me just wants to see Anna Karenina as many times as possible.)