I was under the impression that it was because there are no airbenders to take part in Pro-bending.
Aang was the last airbender, and so now his children and grandchildren—Tenzin, Meelo, Ikki and Jinora—are the only airbenders alive at the moment. And none of them are about to take part in Pro-bending at the moment.
I think there are no air benders in pro bending because.... get this....
There's four of them alive.
I think their names are Tenzin, Meelo, Jinora, and Ikki.
If there are any more, we don't know about them, but I'm sure that they would've been brought up by now.
The first logical answer here.
There are no airebenders in Probending because there aren't any airbenders!
The only airebenders are an old guy, his three young (eventually four) children (the oldest is probably only 10 years old), and the avatar who is already playing as a waterbender.
Besides, the game was created back when there was only 1 or 2 airbenders, even if there were enough, there aren't any rules to accommodate them.
1: There are no Airbenders besides tenzin, his kids, and soon korra.
2: tenzin's too old, his kids are too young, and korra don't know it well enough
3: there'd be no corresponding airbender to even out the game
4: it'd be WAAAY too easy for an airbender to knock them off the ring.
You saw ittle wittle jinora make those wind doors spin buckwild, imagine what she could do to 3 people on a plane above water.