Failed engineer ???
When a board planes we assume it planes on the surface.It doesn`t.It planes just beneath it, in a process called "momentum exchange". Water is moved by the board.When sufficient is being moved and enough momentum generated by its movement to balance the static load. (Weight) planing starts to happen.At low speeds large amounts of water are moved off slowly.At faster speeds smaller amounts of water are moved off much faster.Balance must be maintained against the unchanging static load so board planes on smaller and smaller area but moving water away quicker and quicker.
A wider board will initially move larger amounts of water;its why it planes earlier, but once planing it will also (at equal speed) sit shallower than its narrower counter part.(It will be moving a wide but shallow cross section of water) In other words at any given speed the narrower board will plane deeper and hence have more lateral grip consequently needing a smaller fin.
(But dont bring water line length into it !! It complicates the issue but with boards the water line length is more or less (relatively) equal. (compared to larger craft)
If anyone doubts board does not plane under surface go water mono skiing and look how deep ski sits;it cuts a deep groove.