They do. I have one on my element. Here are the options:This whole conversation has gone WAY off rails because you're making one big wrong assumption. There's no such thing as a class 3 hitch for an Element. There are class three hitches, but as soon as you mount it on an Element, it's only as good as the sheet metal frame that it's bolted to.
I agree that paying Honda $600-800 for an undersized drawbar hitch is stupid, but you can't expect a standard class three hitch to suddenly turn your Element in to a more capable towing vehicle.