One telling quote from Ray's site discusses both the puncture resisitance of foam and the weight problem:

"A foam core can add tremendous bending strength to a lay-up. So in theory it allows thinner, and therefore lighter inner and outer laminates. However, it does virtually nothing for abrasion and puncture strength. The 1995 kayak could be jumped up and down on, but we could have run an ice pick through it with very little resistance. In the water it was battleship strong, but ashore we had to be very careful not to puncture it with rocks, or grind it thin by dragging it over the sand. During the expedition we realized that we should have reinforced the hull with a few extra layers, for that needed abrasion and puncture resistance. This would have strengthened the hull and in fact largely obviated the need for its core."

And also

"The main disadvantage of most types of structural foams is that they add weight. Not just their own weight, which is minimal, but the weight of epoxy which absorbs into them, in some cases like a sponge. To the boat builder trying to minimize weight, epoxy is like lead. Eight or nine pounds a gallon, a gallon or three can soak into Airex or Divinycell core during the lay-up of a kayak and disappear altogether. Among the trade secrets for minimizing resin absorption, perhaps the best is to iron these foams with an ordinary household clothes iron, minus the steam, then prior to lamination coat the foams with a layer of micro-slurry (epoxy mixed with one of the light-weight fillers such as microballoons). Slurry is more viscous than straight resin, and tends to clog the foam's pores. Yes, the internal cells are closed, but the exposed cells have been cut open during the bread-slicing process of manufacture. The slurry technique is to squeegee it on rather forcefully, then squeegee what remains at the surface back off. Then paint the slurry with a thin coat of resin before adding the laminations."