PG,
I could not use less detergent than none at all!
However, if I did use detergent then there would be less in the water to inhibit the action of the detergent, after all, the hardness of water used to be measure by the amount of 'Standard Soap Solution' requied to produce a lather but the cost of purification would probably ouyweigh the savings in detergent.
Purified (demineralised) water, if we get down to splitting hairs, would leave the carpet slightly cleaner but something very much more sensitive than the human eye would be needed to determine the difference.
John