With Raava and Vaatu, light and dark cannot exist without the other. They can defeat each other, yet the vanquished will arise from the victor.
Harmonic Convergence is where spiritual energy is amplified and, as mentioned by the Lion Turtle that talked to Aang, "before the time of the Avatar we bent not the elements but the energy within ourselves" which suggest that bending is a type of energy.
Since this energy seems highly compatible with spirit energy, as demonstrated by Wan's ability to bend all four elements due to his connection with Raava, it would make sense for Harmonic Convergence to amplify the bending energy throughout the world.
As Barry mentioned, there was a great imbalance among the nations. Since the elements, like light and dark, cannot exist without each other, it is natural that airbending emerge from the other three nations to assist in re-balancing the world.
The other three elements already exist and do not need a rebalancing, although a few people may have suddenly found themselves with new bending abilities.
Irrelevant Note: Sorry for the much delayed reply to this post, but I'm recently looking at this stack and I quite love Avatar :)