You know...
The whole point of the original whitening solution, was to take advantage of the Phosphorus Content, or Phosphates in the automatic Dish-washing Detergent.
Thing is though, most powder dishwasher detergent, now-a-days, use a Oxygen Based bleaching system a (sodium percarbonate) which when combined in a chlorine solution, neutralize each other. Plus, the Enzymes in the DW Detergent get killed off instantly in the oxidizing environment...
As for Finish (Electrasol

) Powder itself, the Formulation (pre-phosphate ban) was Sodium Hypochlorite & 3-4 % Phosphate. Now the Current Formation is a Mix, of Sodium Carbonate (washing soda), Enzymes (Incompatible with Chlorine), and Sodium Carbonate Peroxide (stabilized Sodium Percarbonate,Oxygen Bleach)
Borax itself, actually, breaks down into a weak Formulation of Oxygen, which would also neutralize, and ruin the whitening effect of the Chlorine.
From a Chemist Stand Point, this Formulation is very flawed. I don't understand, how the amazing whitening effect would take place...