Think about this for a minute.
Water is used by the Avatar but Ice is never used
Earth is used but metal bending isn't
Fire is used but lightning is never used but can be channeled.
Air as far as I know has no 2nd ability.
To master these elements surely the Avatar must master the 2nd abilities of the elements after all all the "Masters" of each Element have mastered the secondary ability.
Should we see the avatar learning to bend Ice, Metal and lightning or is that asking to much?
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You can master deeeeeez nuuutz