..pressing the first trigger, the hand could just easily slip down, and keep comfortable grip for pressing the second trigger. This is not so with pistol grip.
I have to disagree with this statement, as a flat absolute. It is entirely dependent on the degree of angle of the pistol grip, and, of course, the individual gripping it.
I have my Grandfather's Ithaca double, its having its 105th birthday this year, double triggers and pistol grip stock and all.... and its not at all difficult to work the rear trigger.
Pistol grip stocks are not always more comfortable to shoot. It depends on many things, including the specific user. One of the worst pistol grips I ever found, for ME, is on the Swiss K-31. It's simply too fat for me to comfortably take my usual grip. Nearly cramped my hand, until I realized why...
The main advantage to the pistol grip (IMHO) is that it gives you better purchase on the stock than a straight grip. It gives you something to pull against, when pulling the stock against your shoulder with the shooting hand, which the straight grip does not.
This is more important to target and hunting shooting styles, than it is to warfare. Oh, it works in war, too, and anything that aids in accurate shooting and does not detract from some important ability doing so, is a plus. SO, you see the eventual domination of some degree of pistol grip on most stocks.
and, its a virtual necessity on strait line stocks, even if it is one of the "evil" features the anti gun bigots fixate on.