Karin is a chakra detector, why didn't she detect it then? I don't know. You should ask Kishi. It is obvious the author didn't intend it to go this way, hence he never touched that part. The point is how the battle ended, not how it was going on in the middle or the beginning. Going by your logic, Neji won his fight against Naruto, since he was kicking his ass in the beginning, Kakuzu won, he was kicking everyone's ass, Kiba won, Sound ninja won against Sasuke...should I go on? It's how the fight ends that matters, and Amatersu steered the course of the battle. Hachibi was burning, Bee would have died, no one would have saved him. Team Taka themselves were brilliant. Sasuke was over-confident in the start, think he could take on an 8 tailed beast. He learnt his lesson, improvised and fought back.
If Bee would have appeared again, Sasuke would have taken him on with Amatersu, as he awakened it when Hachibi appeared. He could use genjutsu to knock Bee off for a few moments and attack him. Bee was exhausted. He used up ALL of his own chakra to go into a full transformation. While Jugo completely replenished Sasuke's chakra. It would take time for Bee to replenish his, and he WON'T be able to transform again for some time BECAUSE he reverted back to his human form to escape Sasuke. Which part of all the points in so foreign? Sorry, but get over it comment, you should apply it to yourself.
That is a what if then. If Sasuke used Amatersu earlier, the fight would've ended there and then. But I am not using this logic. Sasuke didn't use it, so this could have should have doesn't mean anything. He almost got killed twice, that is logic, Bee almost got killed once because of Amatersu, that is what the manga portrayed.