Here's a visual of something that is atypical of Shaw in terms of his lack of attacking aggression.
1. Sanchez has the ball on the left of 18 yard. Shaw's current position is behind him. If that's Alba or Robertson, he's running outside of Sanchez.
2. After two seconds, Shaw hasn't read the situation and made the overlap for Sanchez. In fact, he's actually stepped backwards and outwards, but again, the opportunity is very much there for the overlap.
3. In the end, Sanchez gives up on anticipating Shaw's overlap and plays a square ball which leads to a cross from Shaw which is subsequently cleared rather easily.
I want to be able to say that the above is untypical, however, this is something I've seen from him very often. It's less of an issue with Martial playing because Martial holds the width and Shaw isn't expected to overlap, although, there's no reason why a full-back can't underlap in the channel, since this is quite common in modern football.
When Coutinho drifts in, like Sanchez, Alba guarantees to make the above overlap. Likewise, when Mane drifts centrally, Robertson is guaranteed to make that overlap. Arguably, both the aforementioned not only make the run, but they sprint into the overlap to make it all the more effective.
Shaw is guilty of two things, usually.
1. Not overlapping with aggressiveness when the situation clearly presents itself.
2. Rarely sprinting off-the-ball to make the overlap effective as possible when it does occur.
Shaw isn't slow. In-fact, when he sprints he's incredibly quick, which is all the more baffling when you consider that you don't see many offensive sprints from him, compared to defensive ones.