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Neither Avatar in the series ever came close to being Master of All. They learned to use all four elements, but they never surpassed the specialists in their own field - for example, neither Aang nor Korra would ever come close to Toph as an earthbender, or pull off the firebending that Ozai and Azula were capable of.
It's repeatedly stated that the Avatar is expected to master all four elements. Aang and Korra are both young when we see them; they haven't gotten there yet, but it can be assumed that they have the potential.
I think that the example can stand, but it wouldn't hurt to make this point clearer. Something like,
I'd say the Avatar counts. They're by definition a master of every element. Even if Aang isn't to Toph's level of Earthbending, he's still certainly top-tier. And when you factor in the Avatar State, they're much more powerful than even a specialist in their element.
...and I'm not factoring in the Avatar State because it's got serious drawbacks (notably in the original, transformation time; notably in both, the possibility of Final Death). Anyway, we don't see any Avatars who are, in actual fact, grandmaster-level in all four elements. I also disagree that Aang was, factually, in the same tier as Toph; she seems to be in a league of her own in terms of earthbending skill (being able to earthsense throughout an entire forest, for example).
I can go with hbi2k's version; there are bending techniques that neither Aang nor Korra learned and that it's probable that an Avatar can't learn, but it's somewhat unfair to bring up Wrong Context Magic, and you're right that Avatars are supposed to be top-tier in all elements, whether or not they do match up.
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