Running water gives you a GRADIENT, it i much like recharging batteries, where the curve flattens with time, ie washing gets less and less effective.

Dumping everything and extending time slightly with each water saves time, saves WATER and is the only way such things are done among professional chemists, Mason and others nonwithstanding. In classic chemical analysis, with a rotating gizmo, 3 changes of water is generally held to be enough....

I used to do this for a living, in part of my professional life.