JUST MY OPINION! I don't think the quarter cock notch was ever meant to be a "carry" notch. I suspect the original carry mode was hammer down with firing pin between the cartridge rims. Percussion revolvers had been carried this way for decades, it would have been a very short intellectual jump from "Hammer on the safety pin between the caps" to "Hammer pin safe between the cartridges".
Of course, this was found to be lacking in practice. Its a lot harder to do this with a top strap in the way, and if you don't get it right, the pin can slide across the cartridge base to the primer. With the ease of loading compared to the percussion guns, easier to just carry 5, and slip the 6th in if needed.
The quarter cock notch, IMHO (!) was meant as a safety should the hammer be jarred off full cock with little or no pressure on the trigger, providing a last ditch catch before primer contact. This was a common feature in many military arms of the period, and seems reasonable to me.
I cannot prove this, and is AGAIN only my opinion.