A foam base would require a full solid coat of fibreglass matting and resin on the outside, and then to be fully smoothed with a filler of some form (usually bondo).
It is something that can be done, however since foam does not soak up the resin it usually takes 2-3 layers of matting instead of 1-2 layers when a card stock base is used (since paper/card soak up the resin and become in effect another rigid layer).
This is also why when using foam the fibreglass has to go on the outside - if you try and sandwich the foam between fibreglass and bondo it remains squishy and leads to cracking.
The fibreglass is an uneven surface to begin bondoing on and as such it can take a lot of work to get smooth. With cardstock the fibreglass can go inside which will often mean far less sanding is required as the bondo just has to smooth off joins in the cardstock.