You don't have to use a structural grid of wood, though it's commonly employed this way. The basic problem with these construction grades foams is it's density, which is usually quite low. Because of this, it's not a structural foam, will tend to sheer from it's sheathings and must have the laminate (or something) as the structural element, which is self defeating, as the whole idea is a light weight panel.
If you use a real structural foam, the core (foam) also serves in a load bearing capacity, so the laminates can be thinner, hence lighter. I would consider a minimum 5 pound density for structural foams. The Lowe's/Depot stuff is usually 1 to 2 pound stock. This is an insulation, though can make a moderately stiff panel when sheathed, can't be considered load bearing. This is the type of foam that would require some sort of frame system (laminate, wood, metal, etc.) for it to work in a structural application and probably why it's seen so often.
So, as with most things, it's application specific. You can employ these low density foams, but they'll need support and can't tolerate much abuse, be the core delaminates from the sheathings. As Oyster mentioned, they do work for a cabin roof, if not highly loaded or will be walked on. Grab rails or other hardware on the roof would need structural support, but it does work, particularly with small craft.
I know a few that have made small skiffs, canoes and kayaks from this type of foam, but to get a product stiff enough to work, they end up using as much 'glass, as they would on a single skin 'glass hull, so there's no real weight savings. Lastly, sandwich core builds, require a fair bit of laminate engineering, if you want to get the best from the materials involved. In small craft, it's very difficult to rival plywood, in terms of weight and cost, but in larger sizes, you can make big in roads on the weight end, but as I mentioned, it does require some laminate design skill, if you expect to benefit.