I meant the Averbakh with 1. d4 g6 2. c4 Bg7 3. Nc3 d6 4. e4 e5 which leads to a queen trade after de de.
But in general, the Nd7 KID lines can be employed in various move-orders, f.e. 1. d4 Nf6 2. c4 d6 3. Nc3 e5 which can also lead to a queen trade. That and also the current fashion which does not concentrate on these lines would fulfill the "low-theory" part. If you change the move orders, you will not have opponents who slaughter you in the opening because of the move order.
If I may quote from Emmanuel Neimann from the (nice btw) book "The fianchetto solution" (regarding the Averbakh):
"In my opinion, this is the safest answer to 1.d4 - apart from the King's Indian."
I second that. The fianchetto keeps your king very safe. Consider games in the Nimzo-Indian f.e., where you have to concentrate your forces on the queenside to win a pawn there, while White marches forward with his pawns.
You will not often get mated in the KID. It may be sharp, but usually you are the one attacking the opponents king, not the other way round.
I also think that it is nice to keep a lot of pieces on the board, which helps outplaying the other guy. An opening like the QGD can be "sharp" in a sense that you may end up with an IQP and have to find certain dynamic moves to keep the game balanced and not end up in a nice technical position for White.
In the KID, you can rely on that "certain uncertainness" that White has with his small plus. Even if you play second rate moves or play a bit passive, there is still this dynamic potential that does not go away so easily.
In the end, it matters most what you feel comfortable with. But I hope I have clarified my thoughts and maybe help you a bit