The West Coast Offence was developed to hide the limitations of Virgil Carter, who was the QB that came into Cincinnati after Greg Cook suffered a shoulder injury. Carter was essentially the Brock Purdy of the early '70s. So Brown and Walsh cooked up a timing-based offense to compensate for his lack of arm strength and field-reading ability. In the interests of full disclosure, I didn't know much of this until I watched a video a few minutes ago.
Listen, Paul Brown was an egomaniacal dictator, but his influence on the modern passing game is immense.