I posted a response to the OP’s query when he raised the same on the SH forum, but since this discussion has taken a different turn, I’ll add my thoughts. We have very hard water where I live--high minerality--and using at least distilled water for a rinse step makes sense to me. (I have Reagent Grade I here as well, and understand that as soon as the 5 gallon carboy is opened, it is no longer pure--that labs which rely on it, make it on an as needed basis).
I used to use Dawn as a finish stripper when detailing exotic cars. It did a good job in removing car wax, but was itself not easy to remove. I suppose it depends on the concentration used. I’ve largely depended on AIVS #15, which mandates a rinse, for LPs.
I combine methods-- I use a Monks Omni, which is a great point nozzle vacuum, similar to the Loricraft, and the KL ultrasonic (pre-Chad, with integrated tank). If I don’t preclean a new record and go straight into the ultrasonic, I can find some dark gray powder like substance in the bath reservoir of the KL, which I wipe out with some non-shedding, non-impregnated lab wipes. Typically, I manually clean any challenged record (I buy mostly older pressings), do a vacuum and rinse/vacuum on the Monks, then into the KL. To get that last iota, I can pull the record from the KL after the wash cycle (though KL warns about damage to the machine from dripping water into its electronics), and rather than forced air drying, vacuum dry the "wet" record on the Monks, using two mats to avoid wet platter. This does a better job in my experience than forced air drying. The goal, for me, is to remove as much residue of the cleaning agent/contaminant and the vacuum dry rather than forced air dry gives me another shot at that. I think most dishwashing detergents have color, fragrance and other stuff that is unnecessary to record cleaning, and as mentioned, is harder to remove from a flat surface (car body) than the made for LP solutions (grooved surface); for car detailing, I use water under pressure, which you can do with records too, as long as you rinse in something without the minerality. (For the vehicle detailing, I have a Vevor D/I car wash system with two resin tanks--and a TDS meter-- it does a good job at relatively low cost). As an object lesson, a painted car surface with high mineral content water will show spotting--a build up of the solids in the water. I don't want that on my records.
PS: With respect to older copies I buy, I think a lot of the contamination is previous questionable cleanings with whatever residue is left on the record by previous owners/dealers in an effort to make the record look more salable.