To clarify a bit, formula-plugging enables one to solve a certain set of engineering problems. Being unable to derive the formula can also lead one to mis-apply the formulas. (I've seen this happen multiple times.)

Being able to derive the formulas means one knows their limitations. It also means that one can derive a needed formula when it is not in the book. This means that one can solve a significantly larger set of engineering problems.

In aircraft design, this leads to lighter and less expensive parts without sacrificing strength or utility. It's an objectively better design.

Making one who can do this objectively a better engineer.

My ego is irrelevant.

What is relevant is if one's engineering class consists of memorizing formulas, find a better class that emphasizes the how and the why. Math is a big part of that.