Bay absolutely has a distinctive style - you don’t need to be a good storyteller to have distinctive style. If you’re watching a movie with weird framing and use of negative space, inappropriate handheld and wide angle lenses, and actors breaking the fourth wall by staring straight into the camera, you’re probably watching a Tom Hooper movie, for instance.
I can identify a Fincher from a still photo usually - the contrast and tones, shadow depth etc.
Lindsay Ellis has a good explanation of why Bay is both distinctive when compared to other directors … and terrible, with plenty of visual examples. (And this bit is just on Bay’s framing of shots.)
You don’t even think about establishing shots because they’re such a standard part of film language, but it’s jarring when they’re gone. For example, in Les Misérables, there’s an intimate scene of Eponine’s death where it’s just two people singing to each other…and then at the end, the camera pulls back and you see that they’re surrounded by a crowd of two dozen men watching them. It’s jarring, and completely changes the mood of the scene.