Maybe that is why I read that they make Kudzu "hay", maybe cutting the vines and drying them? Or cutting, chopping, and drying? The dried Kudzu hay is higher in protein than green Kudzu.
Winter die back won't really kill it since it will send out new shoots in spring. It roots off rhizomes, sends out tendrils, etc. Kind of like ivy I guess except worse. I wonder if you could kill it permanently by spraying with liquid nitrogen. Or if it would regenerate when it thawed, like a horror movie. LOL
The patch by & belonging to the dump site...containers that are moved/replaced often, county owned.... Well, it's "big leafed ivy" . Don't blink -- it'll cover you. Maybe an acre of it. Leaves are brown now, they deteriorate over winter & in spring, vines bolt into green growth!! Other than perimeter cutting, I see no attempt at control. It could be harvested by hand but, trees overgrown by it and I'd wonder about snakes.
The feed value is tempting but extremely invasive is scary!! Hard to kill out, too.