Oh give me a break. Lambda calculus was created to study computation. To study computation in a rigorous manner, a mathematical model of computation was necessary. The more complex the model of computation, the more axioms you need. Complex models with many axioms are more difficult to reason about but are not actually more powerful (since they are all equivalent...) With a simple model of computation you can quickly build yourself more user-friendly systems (such as demonstrating how Church Encoding works, then proceeding to use it instead of writing it all out every time). It wasn't created out of some sense of elitism, it was created out of pragmatism.

Do you really think that Alonzo Church made his own work more difficult just to make others feel excluded? That's ludicrous.

... just like Euclidean geometry, it was created by a geometer for "internal usage". I am not contesting the usefulness of lambda calculus in academic contexts!

I am just saying that lambda calculus is not the best approach in an engineering context, because it's too abstract, just like in practical terms, I see little use of Euclidean geometry in proving new theorems.