Some good ideas, but the basic reason for a pistol grip on rifles is because they either are, or are imitations of, full auto weapons. For FA fire it is advantageous to be able to have a stock as straight as possible so recoil drives the rifle straight back rather than causing it to rotate around its own center of gravity with the resulting muzzle climb.
If the stock is designed to be in line with the barrel, a "normal" stock hold is impossible (try it!) and the AR/AK pistol grip is the only feasible answer. Some anti-gun types say it makes shooting from the hip and "spraying bullets" easier, but that is nonsense as well (again, try it!). Since FA fire from a shotgun is not normally an issue, there is not much reason for pistol grip stocks on shotguns, except they look "cool".