Definitely not.
A carbon skin each side of a lighter weight core is utterly conventional, but styrene foam makes for a piss poor core. There are all sorts of materials used, from end grain balsa through foams of various densities, often polyurethane, to honeycomb structures. All these have pros and cons. There is nothing very difficult about building a carbon bass cab per se. The challenges come in building one that is cheap enough and road worthy enough, but still light enough to justify the extra cost.
To my mind roadworthy is the big challenge. I've raced carbon race boats, and they are treated with great care, because a lightweight race boat (and a boat 12 feet by 6 feet by about 18inches deep may come out under 80lbs) will dent like buggery if you're not careful with it. By contrast we want to be able to sling our cabs in the van at the end of the evening, and they can't have any more protection than maybe a cloth cover, because it would defeat the object to stuff the thing in a flight case!
Cost of manufacture is also an issue, because ideally one would want to lay up the back, sides top and bottom as a single unit, but that precludes using prefabricated carbon panels. Also customers are going to demand a mirror finish clearcoat, with all the fibre nicely oriented and neat, which adds more difficulty. This is all very soluble with good tooling and adequate investment, but everything is tending to force both cost and weight up.
I'm comfortable enough with carbon/foam construction, and I've done a reasonable amount of it on race boats, but I don't make my home built cabs that way. Partly because by using sophisticated wood construction I can get lighter than most commercial cabs anyway, and partly because I find building with wood fun, and building with carbon/foam a pain in the neck.