A chief pilot's job isn't to fly the line and make money for the company. His job it to manage the pilots, who fly the line and make money for the company. It's always good to have someone who can walk the walk, but I've had too many CP's that spent most of their time incommunicado because they were doing a job in no-cell land. If you're having a problem on your contract you should be able to call your boss anytime.
With too many companies the CP's position is just an additional duty, so they still have to fly the line just to make as much as their pilots.