I have seen cases where the board holds executives accountable, and that results in a better company lead by competent executives. But that kind of accountability is unusual in small companies because the board and executives are often one and the same group.
If there’s anything I’ve learned over my career it’s that the theoretical structure of a company has no inherent relationship to reality. If the CEO, chairman and board members are all mates then they will pat each other on the back until well after the iceberg has ripped a hole in the side of the ship.