I don't think Yaya will play in league matches unless there's no other choice. He will play in the League Cup or in the FA Cup though vs League 1 or Championship clubs. As for Kompany, I think Pep has no real need for him at this point. I mean look at the squad, Kolarov or Otamendi are doing a good job at center back with John Stones. This could be Kompany's last season at City.
Remember when Pep took over Barca? He got rid of Yaya, Ronaldinho and then Etoo. I think he is also slowly revamping City by removing its influential players. Hart is the first to go, Kompany next then Yaya.
Mourinho should follow this too by removing Rooney, Carrick then Smalling.
I like your explanation, but I dont think what Pep doing in City could be a success way too for Mourinho if he follow the method. So far, Pep succeed to maximize the performance of Kolarov, De Bruyne, Iheanacho, and especially Sterling who didnt play well in last season. Like I said before, most of Premier League coaches have known Mourinho's strategy, thats why Chelsea failed last season. So Mou has to seek a new formation to get out of this hard situation. Mou once to make Casillas sat on the bench in Real Madrid, and it has been proven that the decision didnt give good impact for the team performance. So, I'm pretty sure it will give the same result if he remove Rooney.