These wooden rudders are fascinating. Pre composite, the designs utilized fastenings and the properties of solid wood. They usually shared the load. Much of the torque from the steering in a wooden rudder is handled by the solid wood. In your rudders case, solid wood is the bridge between the torque above, and the rudder area below.

The worst quality of plywood is, it's only 50% as strong as solid wood in handling that torque due to 50% of the grain running in one direction, and 50% (or there abouts) in the other.