They do. You can see it in the photo. But it sits below the plastic rails which go all the way to the board. You stand on the rails, not the foam.
I owned Data's that had the Force baseplate. Rode em a whole year. Dampening what complete shit.
Isn't the EVA foam more of a dampening system between your board and binding and also remove dead zone area? I would think your boots outsole would provide the cushioning between the boot and binding?