Some types of soap are traditionally made from just one fat -- lard soap, tallow soap, olive oil soap, coconut oil soap are four examples.
Some soap makers experiment with a single fat soap to learn more about what each fat does when turned into soap. I think SMF members have done this type of project -- use the search function to find them. Here are two examples on the internet:
http://www.zensoaps.com/singleoil.htm
http://alchemyandashes.blogspot.com/2013_03_01_archive.html
There is a third soap maker "Evik, the Curious Soapmaker" who also did a nice study of single fat soaps, but their website doesn't seem to be functional at the moment. Here is the URL I tried:
http://curious-soapmaker.com/big-test-100-one-oil-soaps-part-i.html This page might be viewable using the Wayback Machine, but I haven't looked to know for sure.
Yes, the properties of a single fat soap can be somewhat unbalanced. In my experience, this can be somewhat offset by curing the soap for longer than usual -- 6 months or even longer. This longer cure seems to help single fat soap have more balanced properties -- best mildness, lather, and longevity. Even so, there tends to be a downside to every single fat soap I've heard about or made.
Of the four traditional single fat soaps I listed -- Olive oil soap tends to have a stringy or gelatinous lather and remains highly soluble in water even after a long cure. Tallow and lard soaps tend to not lather a great amount, but they're usually fairly mild to the skin, especially lard soap, and they're long lived. Coconut oil soap lathers a lot but can still be harsh and drying even after a year-long cure. That harshness can be tamed somewhat with a high superfat, but even so it may still be too strong a cleanser for some (like me).
There are additives you can experiment with to see if you can offset some of the disadvantages, such as using various sugars to increase lather or using various salts to decrease solubility. But that increases the complexity again, so what seemed simple at first, isn't so simple if you start adding these tweaks.
So it's true a single fat soap offers simplicity as a benefit, but whether you like the soap or not is something you will have to try for yourself to know.
