When I 1st learned Kosa-dachi, I never questioned it. I just thought it looked cool.
A few years after I began teaching karate, a student asked me what it was for & I didn't know. With my reputation & ego @ stake, I made up an explanation, "If you lose your balance, you can catch yourself & continue fighting." (sounded OK).
A while back I began to think about Kosa-dachi as it is applied in Pinan Godan (Shito-ryu version) when it hit me. No one had ever explained the "Statue of Liberty" pose to my satisfaction but now it seemed so natural.
(Disclaimer: I'm not claiming that this is the only, correct or best application)
Empi-uchi (elbow strike) followed by Uraken (back-fist) in Kosa-dachi. Pivot w/ L fist below R vertical forearm ("Statue of Liberty" for my kids).
Bunkai: Shoulder throw.
Explanation: Launch R elbow to the ribs w/ an immediate R backfist to the nose. Your L hand is grabbing his R arm/sleeve. Your R arm then slides below his R arm pit as you pivot. You are now in position to execute a shoulder throw by pulling his R arm down as you "bow" & lift w/ your legs/hip.
Q: "But what about the next Kosa-dachi w/ Juji-uke (downward X-block)?"
A: "It's not a piece of the previous bunkai. Anyway some perform it w/ a jump, others don't."
The pivoting (unwinding) action is also relavent in the opening move of Bassai-dai. (if you don't get it, I'll tell you later...this is too long already)