Col. Colt seemed to have a love affair with his stocked revolvers but many of the people who shot them had different ideas.
They, like shooters today found that holding a Colt pistol that close to their faces when they fired the guns was more than a bit unnerving. Bits of cap fragments, fire and smoke could cause damage when the gun was held 1 foot in front of the shooters face and that's about where it is when you shoulder the pistol with these stocks attached to them.
Also, the only way to support the gun with their free hand was to support the wrist of the shooting hand. The blast of flame and sheared lead from the cylinder/barrel gap that flies out of both sides of the gun could damage anything held in line or in front of that gap. Then of course, chain firing could really damage a hand if it was any place in front of the cylinder.