And what does this prove? It's worked just like Gaara's sand, a temporarily defence. Naruto could block it with his cloak for a moment, but he had to throw it away, because it would burn through it.
Are you stupid? Do you think he was going to fight with fire on his arm for no reason? He was low on chakra so it's not like he could've sustained t he kyuubi cloak for very long.
Anyways, he threw it away because it's dangerous and could catch the other parts of his body on fire. It could also block his vision in hand to hand combat. There's lots of reasons. Never have I heard of someone fighting with fire on their hand.
Naruto could've kept it on his hand for as long as he wanted