I am not going to say that I have the data but from what I remember that was not identified as one of the causative concerns in the book.

Subjectively I doubt that that is a systematic driver of income inequality. For example in 60s the taxes in the higher margins were extremely high (80% I think?) and worker bargaining power was strong. Yet it was a period of unprecedented growth and innovation, one where ideas of invisible hand and tide that lifts all boats were forged but in reality it was not a laissez-fair period at all.