...removing glycerin from soap to get a longer lasting bar as the glycerin is responsible for the 'mushyness' if left in humid conditions or too much water, but why would we want to remove the glycerin otherwise?...
Not sure where you've come up with the idea that removing the glycerin is
the solution to preventing mush. Soap is a salt of fatty acids and sodium hydroxide and soap is soluble in water. It's going to dissolve in water whether the soap contains glycerin or not.
The choice of fatty acids and the way the bars are produced are more important factors that affect the tendency of soap to become mushy. But there's no way you can entirely eliminate mush if you want soap to function as a cleanser.
Any solid cleanser, whether real soap or a synthetic detergent cleanser or a blend of both, will get mushy if it is not allowed to dry out between uses. Buy a bar of commercial soap (usually contains no glycerin) or any syndet cleanser and leave it in a puddle of water. You will learn these products get mushy too. Removing or reducing the glycerin might slow the uptake of water into the bar somewhat, but it is not the ultimate solution for the problem of mush.
Glycerin is removed in most commercial soaps because they're made with a "boiled" process that uses an excess of water and lye during the saponification step. Historically, the glycerin in this excess water was recovered and purified because it was a valuable commodity that increased the soap maker's profits, not because the soap was improved by the removal of the glycerin.
If you want to remove the glycerin in soap made with a hot process or cold process method, it can be done, but it's truly an optional step that doesn't necessarily improve the soap.
