Evening out the battlefield was exactly what I was going for by proposing the gun. 
Of course this might send us a hundred years or more into the future (the world leapt from basically medieval(except for the fire nation) to late 1800/early 1900-tech in the series pretty darn quick). With inventors being benders or helping them development could even go much faster than it did for us. 
Closing distance as a means to deal with firearms is a definite maybe. The thing is that you can't react to a bullet like you can react to an arrow or thrown weapon. At most I think you can move irregularly, hope that the shooter will miss and/or run out of bullets. I mean, an olympic runner can run 100m (around 300y) in just under 10sec if he does nothing else in his life and runs in a straight line, an old six-shooter can be emptied with relative accuracy in half that time. 
But I guess all arguments can be turned around like this, it mostly comes down to if benders over all like or dislike the idea. If benders don't like the idea of guns then the inventor would have a really hard time. If they like the idea then I guess it would be developed in a week, haha.

I actually think I remember Katara stopping a few arrows with frozen water, Longshot (in Jet's gang) and of course the legendary Yuyan archers use archery, so there is a definite opening for ranged combat. Many of the bending-tricks used against guns can also be used to stop arrows.

The equalists tech felt a bit off to me. It just felt stupid that the best way to counter benders was to best them at their own game. I would've liked the "normal" people to come up with a way that allowed them to truly surpass the benders. But I guess that wouldn't have been as cinematic.