Snowfoam isn't designed to move grime off but to make it easier to get it off.
The idea is to soften up hardened dirt, to try and lift some of the dirt off the surface. This means when you go over with a wash mitt, you don't marr the paintwork.
The entire point of snowfoam, microfibre wash mitts, two-bucket method of washing etc is to reduce the damage that washing inflicts on the car. The 2BM should still be the mainstay of washing your car. Presoaking with snowfoam etc is designed to make it easier and less damaging.