Actually, come to think of it, kudzu is edible by humans, and, I think, is eaten by them in Asia, from whence it came.
It is eaten deep fried every year at the Kudzu Festival in Waxhaw, NC.
The leaves are indeed edible, but not all that tasty and rather tough. Kudzu starch from the roots is highly coveted in Asian cooking and is pretty pricey when you can find it in a specialty store. Personally, I'll stick with arrowroot starch from Penzeys (far superior to corn starch).
No kidding though, goats love kudzu and are very good at controlling it. You would need to supplement their diet, however, to keep the critters in optimum health.