I found a post on another blog about one shaper who is making alaia boards out of thin pieces of wood and foam. This "sandwich" construction is described on the blog as follows: "The Alaia-Lite has a foam core, wood sandwich construction, made of locally harvested and reclaimed wood from Hawaii." Bravo for the use of reclaimed wood, but this seems to defeat the entire purpose of the alaia movement, which is to return surfing to its historical roots and to be able to make a board from a single, sustainable material.
The maker of these alaias says that the use of foam enables the boards to float better and permits people to more easily catch waves, since an all-wood alaia does not float very well. This, I can see, is a benefit of the use of a foam core.
Nevertheless, for now, I'm sticking with wood.