The original foam, even in excellent condition, is fairly thin and soft with a "skin" layer on one side.
As it deteriorates, the "skin" becomes sticky and the foam turns into gritty particles. The advantage of re-using original foam is that there is little pressure and re-assembly is probably easier.
A sturdier, thicker new foam will add compression, possibly increasing the springiness, but will also dampen sound and vibration. I would consider that a good thing. It also makes re-assembly harder because you have to use more force to press the plates back together. Using clamps, it is no big deal, but it would be extremely difficult to re-assemble by hand alone with thicker firmer foam.