"...I'm curious if you have any thoughts on this?..."
That's not a direction I feel any need to explore. Assuming I wanted a cleanser with a pH similar to the outer layer of skin (about 4.7) or even something like a pH of 7-ish, I'd be formulating with detergents that have a normal pH in the desired range, not trying to force soap to be something it's not.
Research is showing that any sort of cleansing, even with "low pH cleansers" or just plain water, disturbs the pH of the stratum corneum (the skin's outer layer) for some hours after washing. Other recent research is starting to look at people with normal skin and the results show that most people most of the time are just fine with most soaps. Unfortunately a lot of dermatological research is done on people with unusually sensitive skin, not normal skin. Researchers are generally NOT interested in knowing about the average skin of most people; they are interested in finding statistically significant differences by testing people with highly sensitive skin.
The pKa of fatty acids commonly found in soap is 7.5 (pure lauric acid) to 10.2 (pure stearic acid) with the others lying somewhere in between. To explain, the term "pKa" is the pH of a special kind of soap mixture where there are equal numbers of molecules of a pure fatty acid and the soap made from that pure fatty acid. This isn't a "real" soap as we would normally think of soap because the amount of fatty acid is pretty high, but the pKa gives us some idea of the lowest pH at which a soap mixture actually starts to act like "real" soap. So even if you could make a soap from pure lauric acid, the very absolute lowest pH that you could get and still have something that's kind of soapy is 7.5.
The other pure fatty acids ... and any mixtures of fatty acids as you would find in a normal handcrafted soap ... are going to have a pKa of just over 8 ranging up to just over 10. Again, remember the pKa is the LOWEST possible pH of a "soap" that is going to vaguely act like a soap, but it's not going to be a pleasant soap that most people would really want to use. If you want a soap as we would normally want it to be -- a product with good lather, decent cleaning, reasonably hard, not greasy feeling, etc -- then the pH of that product is going to be higher yet.
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"...what the purpose would be to add citic acid or vinegar (and subsequently extra lye) to a recipe if the two are just going to cancel each other out?..."
Carolyn nailed it! They don't cancel out exactly; they create a salt.
NaOH (sodium hydroxide, an akali) + HCL (hydrochloric acid) => table salt (sodium chloride, NaCl)
NaOH + Citric acid => Sodium citrate
NaOH + Acetic acid (vinegar) => Sodium acetate
NaOH + Ascorbic acid (Vitamin C) => Sodium ascorbate
All of the chemicals on the right hand side of the => sign are "salts" that are produced when a base (an alkali) reacts with an acid.
Salts can do different things for us that their alkaline and acidic parents cannot. Table salt can flavor our food or harden our soap, but its parents -- hydrochloric acid and sodium hydroxide -- will burn our skin terribly. Sodium citrate can prevent soap scum from forming if you have hard water.
