if you're using quality pre-spray in sufficient quantity and dwell(or mechanical agitation) you only need a slow back flush stroke.
in that scenario, a forward keys stroke only makes carpets wetter, not cleaner.
it's easy enough to see for your self on the next trashed rag you clean.
if you see a difference with a keyed forward stroke, it's because you're using poor pre-sprays, not enough pre-spray and dwell time and the wand agitation is what's making the difference.
not the added water.
if you don't use quality pre-sprays in suficient quantity, or run just run emulsifier thru the wand to clean, then you need a keyed back and forth stroke
..L.T.A.