Much wider width than chord
Width (street speak) is the chord (tech speak). Do you mean that the rudder should have a much
thicker section compared to the chord than the centerboard? That makes sense.
In general, thicker sections have higher drag but have higher stall angles. Since the rudder may be suddenly turned by a large amount (coming about, collision avoidance, etc.) it is important to have a foil shape that is resistant to stalls. A stalled rudder will contribute to drag but not to rotational forces needed to turn the boat.
There is a tradeoff then between a thin, low drag rudder that may easily stall upon application of large inputs and one which is a thicker (higher drag) shape but able to take greater control inputs without stalling.
Optimum is defined only for a specific case. Do you want fast to go fast in the straights, or do you want to run the obstacle course, or do you need some measure of both? Yous pay your money and yous takes your choice.