Do you have any evidence that Euclid disagreed with me? Elements starts off with a list of postulates, definitons, and common notions. Then he proceeds to proposition 1. He does not motivate why one would want to come up with proposition 1 or why would should care about it. Have you read Elements?

How do you propose one do applications of point set topology without knowing about sets and mappings? Before the applications one must know the language. We don’t teach the quadratic formula and solving simple velocity problems before teaching students how do the basics of manipulating algebraic expressions.

One must first be a baby before being an adult.