Okay, now I'm blushing...but let's get on with the answer! There are a few reasons for using stearic acid. (And I think this applies to cetyl alcohol as well!)
1. It's a thickener. Although you can reduce the water or increase the butters to get thickness, stearic acid is a quick and easy way to add the thickness. And you need less stearic acid to thicken than you would do butters. 3% stearic acid can thicken better than say 10% butters.
2. It's inexpensive. Butters might be $20 a pound, whereas stearic is rarely over $5, and usually less. So adding 3% stearic acid is cheaper than adding 10% butter.
3. It has a long shelf life. Yep, most butters do, too, but we know our creation will have at least a two year shelf life using stearic acid.
4. It gives body to the recipe. For instance, I found a beautiful recipe on the Dish for a whipped body mousse. It has very simple ingredients - oil, emulsifier, water, preservative, and stearic acid. Without the stearic acid, we would have a very light lotion. But stearic creates a thickened, mousse-y quality to the lotion that we wouldn't get otherwise. A butter would weigh it down, so stearic is the best choice.
5. It's also an emollient - stearic acid is a great softener - and to get 3% into a recipe using butters you'd have to use at least 10% shea, cocoa, or mango butter. You can use it in a lotion and call it "oil free" because it's not an oil, it's a fatty acid.
Having said this, you can most certainly leave out stearic acid and just go with more butters or a reduction of water if you like. Try a little experiment - try your favourite lotion recipe with stearic and another version without. It's easy to see what the stearic brings to the mix: It offers a stiffening you don't see with the butters. The butters add emolliency and stiffening, but add a little greasiness; stearic acid adds emolliency and thickening without the greasiness.