@Hendejm's description most closely fits how I think about all this. Here's why.
I had been washing my face with the same soap for about 7 years, but last year my lower face started pulling into weird 'folds' after washing, which I would then get rid of with my moisturizer -- hopefully before anyone saw me!
When I joined SMF and started seeing that coconut oil was highly stripping (cleansing), I knew I had to get rid of my beloved coconut oil based soap. However, I thought that I "should" stay kind of middle-ish on the SoapCalc numbers, and also felt I needed coconut for the hardness and bubbles. I've laid out all my soap properties and formulas on an "at a glance" sheet, so I know that my soaps 1 through 9 have cleansing numbers of 17, 16, 16, 18, 14, 14, 13, and 5. (Yes that's 8, not 9. My 8th soap was never intended for use, only for the Feb challenge. And yes, it took me a frightful amount of time to reduce the coconut oil enough!!)
I've not had the chance to try the C-5 soap yet, it's 10 days old today, and just made my 10th batch at C-0 (which really isn't true, but SoapCalc doesn't handle Olive Oil correctly, at least in terms of the cleansing #). But I have tried all the other soaps. This is what happened:
All my soaps have ameliorated the weird alien-face pulling, but I still feel varying amounts of tightness. After washing my face with the first few soaps, there was a short delay before some tightness set in. With the C-14 and 13 soaps, there's a longer delay of 2 or 3 minutes before I have to reach for the moisturizer. I am expecting that with the C-5 and C-0, whether I moisturize will become a choice rather than a necessity. Why? I've had plenty of my own skin oil most of my life (Sicilian = grease bucket!!), and still have more than some people regardless of age. It is appearing that, to the extent I can leave my own skin oils intact, my skin feels not necessarily moisturIZED, but still moist -- or what's that word having to do with oil? Has an emollient feel, maybe. I think it just doesn't feel dehydrated, as I get closer to my ideal soap formula.
The oils in soap are no longer oils after saponification, and my SF is kept in the 1% - 3% range. [Most of the time, only 1 or 2% to ensure I never have a lye-heavy result.] What I mean is that, in my case, I don't think the beneficial result is a function of what oils were used or traces that may remain, but of gentleness and
less disturbance to the oils which are part of the skin's protective
acid mantle.