Avoiding the eyes would leave ALL of them open to Amaterasu, not that they would be able to react to it anyway. This absorption would only work if anyone is able to sense Amaterasu and we saw it in Nagato versus Itachi fight that he never saw Amaterasu coming. Since he can't sense it, Petra Path cannot react to it, and if he cannot react to it, he is taken out. The second any path is revived through Nakara path, he will be obliterated the next second.
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- CT can be destroyed by aiming at the core. A few Enton arrows would take it out.
Using God-Realm/ Deva Path's high tier abilities - Almighty Push and Chibaku Tensai - would make the paths recovery speed much longer :
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and
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- that would leave them completely open to attacks. Meaning, they will be taken out easily this way.
Not only that, Deva path cannot even use Shinra Tensai and Bansho Tenin if he uses Almighty Push or Chibaku Tensai for quite a while as we saw during his battle with Naruto that he was unable to use both of them for quite some time:
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.
Itachi was able to hold his ground along with Susano'o even with CT core's immense pull, do you think BT would pull a level 4 Susano'o towards Deva? Come on.