As several people have mentioned, this is a technique known as "ragging". Twenty or more years ago it was the accepted method.
IT WORKED THEN AND IF WE COULD STILL GET DECENT SCRIM IT WOULD WORK NOW
A very slightly damp "proper" scrim would clean and polish in one action with a bit of elbow grease. It removed the dirt and left the glass sparkling. There was an art in wringing out a scrim to just the right degree of dampness.
Modern rubbish sold as scrim will always leave streaks if there's the slightest hint of dampness in it, so I'm afraid you youngsters will never be able to "rag" your way around your work.
Years ago I never used anything except scrim, and the results were always perfect. I took a couple of years off to do something else and when I came back proper Irish Linen scrim was no longer available, just hopelessly inferior middle eastern stuff.
WFP is a brilliant invention, but sometimes I hanker for a bit of proper scrim and a chance to show what I can do