I have strongly advocated such separation for 40 years. The reason is simple. The two functions are different and usually in conflict.
The chairman of the board is responsible for the operation of the board and the board itself is responsible to shareholders for the operation of the corporation. The board must be the entity that chooses and determines the compensation for the chief executive officer.
These are two distinctly separate functions. In the past 20 years they have been conflated and we have gotten hundreds of the top corporations where the title is Chairman and CEO. As a consequence we have gotten executive compensation that is disconnected from the performance of executives.
I think we would have a better chance of controlling executive compensation that is disconnected from performance if we begin by separating the function of chairman of the board from the function of chief executive officer.