Not true. I have an RC model airplane which uses a pink foam core with no shear web, even though it uses carbon pultrusions for spars. It has no problem with a hard pull up at 50 or 60 mph. The Sky Pup, an ultralight aircraft that people have been building for years, uses blue foam as a shear web in the wing spar. A cantilever wing, no struts. Apparently, there has only been one structural failure, and that one was AFTER a crash.
Dow has Highload foam in 3 types, withstanding 40, 60, or 100 psi. The latter's compressive strength is getting close to that of a light flavor of Airex. I'll admit I haven't looked it up, but I suspect that the shear strength is much more than the regular stuff, too. Highload 60, at least, is not that much more expensive than blue foam. Highload 60 is only a little denser than regular blue foam, I think something like 2.4 lbs per cubic foot, and Highload 100 is significantly denser. 4 lbs? I'm guessing that other brands have foam that can take similar compressive loads.
I think if the skins are sufficiently resistant to abuse, they will be more than adequate for bending loads, and most loads, except maybe around engine mounts, deck fittings, etc.. If it was my project, maybe I'd use Highload foam 1/2" thick, because thicker would probably be overkill. If I wanted buoyancy, I'd probably mostly use air chambers, since air is a whole lot lighter and cheaper than foam. A guy who builds fiberglass boats with foam cores told me he would use about 18 ounces of stitched biaxial glass for decks. I don't know how strong the foam he used was, but it was some other chemistry, not polystyrene. Don't count on this without verifying. For instance, I might not have noticed if he used some other layup for decks; I think I was only helping him with the hulls. It was a long time ago.
Anyway, I think the structural issues are quite solvable, although MAYBE it would be necessary to use something a bit more substantial than Foamular 150, which, if I recall, is only good for 15 psi in compression.
I'm more concerned about what gasoline does to polystyrene. I think it's supposed to just melt the foam and turn it into goo. Also, if the foam gets too hot, it will soften and melt. I had a set of foam cored, carbon/epoxy covered wings. I had them in what I thought were opaque wing bags, which turned out not to be true. When the sun hit them for a few minutes, part of the foam core melted. There's a reason all those VariEze and LongEze homebuilt airplanes, made with blue foam, are painted white. If memory serves, I think the service temperature of Dow Styrofoam is something like 160 degrees F.
The other thing I don't really get is how this boat will be better than someone's old, beat up aluminum jon boat. Maybe it could be lighter, if engineered properly, but fiberglass is heavy, floppy stuff compared to some other materials. I could see using thin ply over a foam core...
