The Wenger problem is largely that his methods are incompatible with the modern game. It's not only the transfer stuff anymore. What was once innovative on the field no longer is. What's innovative now is the way City is planning their attacks. Whenever they get the ball, Aguero is showing to midfield along with a midfielder pushing up to receive the ball from him and immediately spread the ball to the opposite side. Liverpool and Tottenham do the same things, United doesn't, but they get points due to defensive solidity, because their coach does know how to defend these things. Wenger's defensive organization is pretty much laughable and the coach has no idea to prepare his defenders to deal with repetitive, rehearsed attacking movements. Their defensive line is almost at midfield every time Aguero receives the ball, there are no midfielders between City's primary attacking plan and the goal. Actually surprised they didn't score more. The only chances Arsenal can count on getting are from outside the area and defeating an athletic goalkeeper like Ederson from there is going to be very difficult.
Wenger's had the same coaching staff at Arsenal for ages, which is another problem entirely. He has nobody to tell him what top clubs are doing on the training ground and seems genuinely oblivious.