I have not claimed he has control over what happens on the pitch. I questioned if it was believed that the manager bears no responsibility for it.
Seeing as the manager picks the team, selects the squad, directs the coaching and decides how to spend any transfer funds we may have (all of which will influence what happens on the pitch), then he must bear some responsibility for what happens on the pitch.
If the manager doesn't do anything that influences what happens on the pitch, what exactly is his role?