I have a theory as to why Mosconi and others used the slip stroke.
In his book, he mentions placing the grip hand 6 to 8 inches behind the physical balance point of the cue.
As you know, the cue's diameter gets larger from the joint to the butt capp. It may very well be that Mosconi's hand, when thumb tip touching middle or index finger, would work out to the "sweet spot" of his cue. Therefore, it would be logical to utilize a slip stroke during the back swing of the stroke. One might suggest that the slip during the back swing is to set the grip position, and the slip during the forward motion is the byproduct of the loose grip.
I have played with both. The slip stroke, the stroke slip, and both during each shot. I don't see any significant advantage to the techniques. I think it is a matter of preference.
I can tell you that the double slip is not easy at first, but once you get comfortable with it.....the stroke feels good. It's kind of like driving on a wet road, you peel out at the start, hit the brakes, and slide a little.
The slip stroke is also sometimes used during power break shots. Some people recommend placing your grip farther back during break shots. If you address the shot normally, then your aim will be set....then using the slip stroke during the back swing you are effectively placing your grip farther back. But instead of doing it from the start, you are doing it during the Break Shot stroke.