Steve

 

You can't just assume that though, perhaps it would damage it over time but if that's Yama's strategy then they'd both die it kills him too.

Amaterasu being as hot as the sun is still an uncontested statement if Yama can contain his heat and environmental damage can be negated with it the same must be applied to Amaterasu which even when enhanced only really annoyed the Juubi. Just because it's plant based doesn't mean fire is it's weakness it's not a Pokémon.

That enhanced massive Rasenshuriken enhanced Amaterasu arrow only got a bit of it's shoulder which it quickly removed and regenerated, that attack is easily as powerful as a slash from Yamamoto.
Look how big it is
Compared to that tiny toad there who's about the same size as Gamabunta who's also freaking massive and not even nearly the size of the Juubi's head, Yama needs multiple cuts here.

It's worth noting that the Juubi is very fast too, it's not going to just stand in one place the whole time most of the time it's been hit it's been restrained in some way and it moved faster than Kurama could react, he wasn't paying attention but still with his senses he should have had plenty time to dodge were it slow.

It also flicks a Bijuudama back at the 8 Tails with one finger which shows how damn strong it is considering the density of those techniques so there's no way Yama can tank hits from it easily.