No, of course not. Factorial are just an illustrative example.

My goal was to dispel the myth that the lamdba calculus is nothing more than an intellectual curiosity. It is much, much more than that, not because you can use it to compute factorials, but because the techniques that you use to compute factorials in LC are generally applicable. If you really want to master the craft there are a few things you really need to know how to do: write your own compiler, your own editor, your own implementation of the Hindley-Milner type system. Writing an efficient factorial in LC is like that. It's not useful in and of itself, but for what you learn simply by going through the process.