CF would work from a vibration aspect - think fighter planes and stealth bombers, they're mostly composites like CF.
The obvious main reason it won't get used is it would more than double the cost of a conversion. To make structural CF pieces they have to be formed under high pressure and heat, it doesn't work like fibreglass at all. A buddy of mine built a dargster sized autoclave for his brothers CF company so they could make bodies for top fuel cars - major major expense. Also it's conductive and blocks radio waves which would be an issue. So maybe for frame members but not as exterior or interior sheathing. Weight isn't too big a deal, it can't be that hard to soften up the spring rates.
I have to say it woul dbe cool though
