I've heard a number of top teachers say that the hardest thing to teach in golf is 'weight shift'. Swings that one way or another 'eliminate it' are far simpler for most. BGG would be in that category as well as the IMA Impact Backwards drills. HSS also attempts to simplify it by only having your weight go forward.
Eliminating weight shift not only makes the swing simpler but when you keep your weight on your lead foot it is easier to get a consistent bottom of arc at the forward point where it should be. This is why Pelz among others recommends keeping your weight on your lead foot for some short game shots (shots where the power from weight shift is not needed per Pelz). This point is likely why S&T came to this given Bennett's statement in one YouTube clip that one of the things consistent with all pros is their ability to 'hit the ground' exactly where they want (personally I prefer John Jacobs golf swing 'reduction' formula) and their goal was to focus on only those essentials that were consistent with all pros.
Of course the departure with S&T vs BGG and the others I mentioned is claiming that tour pros swing as they teach. All of the tour pros I've heard mentioned that are in their 'stable' were tour pros before they went to S&T so they clearly are able to hit the ground where they want as well as hit the ball far enough to play the course (S&Ts #2 consistant pro element). I've yet to see any tour pros that 'tilt sideways' (Bennett's term) on the backswing and it actually seems that Weir is saying to Gary Player on the range (the clip is on YouTube) that this is NOT what S&T is about.
So I think that eliminating weight shift can be a good thing for ams (and the way I played for a number of years with IMA until I 'got' weight shift) and is likely the thing that will cause ams playing with S&T to do better but the real, though not quick, fix to get consistent contact is to maintain the angle until your hands are over the ball which IS something you will see all tour pros do on regular shots.