Now that the avatar is no longer the bridge between the spirit world and the physical world, the responsibility of being able to give bending to non-benders would make up for that lost responsibility.
I would be interested to see how that would work though since there was a different lion turtle that gave the bending power of each element. The avatar would have to be able to choose which element to give. When Korra restored everyone's bending at the end of season 1, she was only restoring the element they already had, she didn't have to choose which one. If it is possible, my guess would be that the ability would be another technique that is a part of energy bending. No avatar before Aang, or any human for that matter, had the power to bend energy until Aang received the power from the lion turtle. The power gave him the ability to take away someone's bending and at some point he may have learned how to restore it. Korra has the ability to energy bend since she is the reincarnation of Aang. She just may have to learn the new technique just as any other bender would have to learn the techniques associated with their elements.
If the avatar did have that power, it would also mean that other people could be given the ability to bend more than one element. That might be too much power, even for the avatar to have.
I hope we get some information on season 3 soon so we know if energy bending is part of it or not. It would be cool to see but I don't want to get excited for it if it may not even happen.