Oh the irony!
Sterling coming inside for a cut back has nothing to do with holding the width. Of course he will come in from the left when the build up is on the right. When they build up on the left, he will usually be wide.
City play with genuine wingers who provide the width and stretch the play. The central support for the main striker comes from the attacking midfield players. United play with wide forwards who tuck in to link with the striker. The wide player is as likely to be inside the man in possession than outside when they build up down that side (see Pogba's chance at Watford when he played a one-two with the wide forward, Martial, who was inside him). That means unless the full backs bomb on they have no width in the side.
My issue with Shaw isn't how far forward he goes. It's how wide the position he takes up on the pitch. You can see it even moreso when United attack the Stretford End. Just watch how narrow the position is he takes up. Compare that with Robertson or Alexander Arnold who also play behind wide forwards rather than wingers.
I can see where Mourinho was coming from with "I was his brain on the pitch" because, offensively, Shaw has no positional sense whatsoever.