So, you say that palm, lard or tallow make a longer lasting soap than coconut oil? This is my perception too, but I can't explain why.
Not really....
I have no opinion about whether palm oil soap lasts longer than coconut oil soap. As far as I can remember, I've never made straight palm or straight coconut soap. I never saw any need to. I have used soap that had no coconut oil. I have used mostly coconut oil soap as well. Neither was all that impressive.
It takes a balance of oils to produce what I consider ideal soap.
My idea of ideal is just my idea. But I'm making soap to sell, so I'm pretty set on what I want.
The fatty acid make-up of the different oils will give you clues as to which ones are much alike and which ones are quite different.
You can see the differences at
http://www.soapcalc.net/calc/SoapCalcWP.asp.
By the way, some say shoot for recipes with an INS value of about 160. Mine tend to be a little lower most of the time.
Several soap books also go into what to expect from different soap oils.
A soap made about like I suggested will last for a long time.
In my experience, I say a coconut-heavy soap bar will leave a person squeaky clean. The squeak results from complete removal of the oil from the skin. That's maybe not so good.
But if you want top lather, it's hard to get it without coconut or palm kernel oil.
A bar soap can be pleasant to use and still last for weeks of normal use.
I've sold a lot of soap and folks won't be happy and buy more if the stuff just melts away. It has to stand up to use to keep people happy buying it in quantity, or so it seems to me.
Look at the label on a bar of Ivory (coconut// + palm//) or Palmolive (palm + olive ) to see that the giant soap companies also use multiple oils. Look at Octagon soap ingredients and try that out also.
By the way, I've used handcrafted soap that seemed inferior in most ways to Ivory! Not good!
Note that some say that coconut oil makes soap that is hard, but quick to fade away with all the bubbles. I'm not too sure about that. I do know that a formula with coconut, palm and olive can lather like crazy, clean well, moisturize and last a long time.
It's the balance of the oils that is the key. And it does not require complicated formulas to make great soap. You can make great soap with just 3 oils for certain. I think it's tough to make soap I would really like with fewer than 3 though.