How many people can name the chairman of the board at Apple today off the top of their head (Arthur Levinson)? And how much does Arthur Levinson steer the broader direction of the company? That's just not what the role is about.
Steve was so effective precisely because he was able to get deeply involved in the day to day details in ways no other CEO has (whether on product matters, or personnel matters). That's not what you do as chairman of the board.