Back in 1995 I had a brainwave, which was to make the board ( and thus the core ) the same thickness all the way through the length of the board as you have described, in order to make the board flex.
After drawing a profile of a proposed board that way on the workshop floor with chalk, I was horrified, but intrigued, and yes to me it looked pretty ugly . . . but handsome is as handsome does as they say and we went ahead and built the first five parallel profile boards from balsa. . . all 1.5 inches thick and twangy, ranging from 7 feet to 7 ten and all at 18" wide.
The bottom line is that it works beautifully, and we are still doing it 80 something boards later.
The look grows on you , it's like a haiku of surfboard design.
A parallel profile gives a concave deck automatically, at least in the fore and aft plane.
Underway right now we have a 6' x 28.5" wide x 1.5 thick tunnel finned squaretail and a 12'9" x 27" wide x 1 and 12/13ths of an inch thick pintail . . . . IMO those lovely thin thicknesses are only possible with a parallel profile !
, extra thickness added is added everywhere including the rails
