The issue of the rig "pounding" the board is not affected much by the thickness of the board. It's more a matter of having a good connection between the mast box and the top laminate so the forces are distributed through the deck. But when it comes to a pure flat landing from a high jump, a thicker board will hold up better if everything else is the same. But when it comes to wave boards the Starboard have been rather fin for many years and have the lowest warranty rates. And if you think of a board like the Atom, it is still not THAT thin in the middle where a pure flat landing would break it. And like with any boards, the construction is a careful compromise between low weight and the best possible strength.
If you think about the slalom boards, like the iSonics and especially the 86 slim, they have a concave deck profile that actually adds stiffness to the board.
Feel free to ask again if you have ore questions.