Because the airbenders were not only going to have the new avatar, they were the most practical and direct threat to the fire nation as the only other benders not reliant on having their resource within reach.
I know korra get a shit, but if you figure most airbending masters were as good, if not better than zahere, who could go blow for blow with a weakened avatar, that's a serious threat. Hell, aangs master was shown surrounded by dozens of corpses he killed single handedly, and those would have been elite benders.
Not to mention their complete air superiority, and the inability to blockade or fortify against them. It wouldn't surprise me if the reason the air nomads are the only air benders, is because as a violent, nomadic horde they would have presented a terrifying threat that would have United the other nations in their genocide, and some ancient avatar forced them to adopt a non-violent lifestyle in order to maintain their existance.
The water tribe becomes useless was soon as they get to far from water, and earthbenders, while powerful and destructive, are slow, easily out manuvered, and can be blockaded by lava, water, or even thick mud.