Expanded polystyrene is, by design, a very lightweight and flimsy material. And the very fact that it's so flimsy, and also typically used in food containers, is why nobody wants to use it: it tends to be horribly contaminated with foreign material, and is difficult to effectively clean. I'm not sure there's much of a market for a post-consumer material that consists of a mix of polystyrene and uneaten cheese.

Well for one styrofoam is neither dense nor valueable so even if said solvent stew approach could work without cleaning and filtering economically (not a given) hauling a bunch of styrofoam wouldn't be all that efficient compared to even glass let alone aluminum.