Well as others already stated olive oil is one of the major oils in order to formulate a balanced recipe. And it is for the fatty acid profile that it has.
Olive oil belongs to the group of hi-oleic oils among sweet almond, sunflowerHO, safflowerHO hazelnutand and other mid-oleic oils such as avocado, canola, macadamia that also bring similar characteristics in the final soap bar and you can use only these (or part of them) on the average percentage (eg ~40%) that you would normally do for olive oil:
40% olive oil or
20% olive oil +20% sweet almond/avocado/hazelnut or
40% sweet almond/avocado/hazelnut etc...
I had once made an experiment where I used a recipe with other oils and a few additives (as one would make) in which the major oil was a pick from the above hi and mid oleic oils group.
The recipes were:
(High Oleic)
1. Extra Virgin Olive Oil,
2. Sweet Almond Oil,
3. RAW Pomace Olive,
4. Sunflower High Oleic,
(Mid Oleic)
4. Avocado Oil
5. Canola Oil
@ 40%
along with Lard: 30%, CO: 15%, PKO: 10%, Castor: 5%
Later I also created another same recipe but with 40% macadamia.
They were all almost the same at how the suds felt on my skin apart from avocado and especially macadamia that were one level above all others.
The reason for that difference is the rare fatty acid that they brought to the party that is called palmitoleic (C16:1). Avocado has ~9% of it and Macadamia ~20%.
That made me believe that the things that firstly affects the way that soap feels on the skin are the fatty acids and their respective percentage in a recipe and afterwards the additives/superfat.
You can see the video here: