As a fan of Brubeck for several decades, I'm well aware of the criticism he received. But "No soul, no jazz"? I just don't understand that. I've heard plenty of emotion, drive, and thus soul in many of his recordings.
This may be an oversimplification but I believe much of that criticism came from two factors. One, much of his playing was melodic enough (especially when joined by Desmond) that it could be appreciated by a broader audience than just those favoring straight ahead jazz. Thus he was more commercially successful and so possibly resented by those who hadn't reached that level of popularity. Second, I suspect many musicians and critics couldn't accept the fact that he seemed to have come from a music conservatory rather than up from the streets earning his trade in bars and road houses. The latter included those claiming no soul in his playing.
To my ear he was talented as a player, composer, and explorer of new boundaries. He could swing, play ballads, honor tradition with stride references, verge into avant-garde, and how many other musicians devoted as much creative energy into new directions as Brubeck did with time signatures?