For the long term, I think it will never be a successful project unless as any manager (as you put it) has complete control on transfers. He took a big decision by refusing to keep Sterling at the club and the owners backed him therefore he clearly has a lot of control. If they allow him to manage it could be a mutually beneficial relationship but if they control the transfers, it will probably end in an acrimonious manner.
On paper it looks like he singlehandedly made that decision but in reality, it was the board decision to take off every player( Sterling and Chilwell) above the new wage structure out of the project. Sterling only made it easy with bad performance after all the chances he had in preseason.
The new wage structure can not accommodate both players and the management are not ready to adjust. He may likely follow money to Saudi except he's willing to take a pay cut in Europe.