Is it also possible that food-contaminated styrofoam is significantly costlier to recycle than styrofoam on its own, or did this specialized process also take care of this problem?
The problem is that there is no money to be made from selling recycled styrofoam since it is competing with products that are themselves extremely cheap. If we imposed a high enough tax on the original product, then it would be cost effective. However we still have the trouble that we have to collect it, separate it out from other wastes in the waste stream, and so on.
So we could recycle styrofoam. But we don't because it is not cost effective to do so. So it is viewed as unrecyclable. And for that reason we have replaced it with things that are even less recyclable.