It's probably not replying, because you are giving "evidence" which can easily verified, while I am making assertions based on my knowledge of the field, knowledge that you probably won't acknowledge I have because you're already convinced that I'm misguided on this topic. Anyway, all your examples (except for econometrics) are on the fringe of economics:
Linear programming is almost never used, since economists like exact analytic solutions. Maybe it was popular when that Nobel prize was given?
Calculus of variations, optimal control, dynamic programming: yes, although I would not call these applications of deep math. The underlying ideas are very simple, they've just been written in much more general forms for reasons that are unclear to me. But only the simple versions get used. Same applies to fixed point theorems. You might learn and forget these things in the first two years of a PhD program, but that's about it for 99% of economists.
>Smale of Field medal fame used Baire category theory and Sard's lemma to establish a new method of obtaining general equilibria for economic questions. Do those count as deep?
Yes, and almost certainly useless for econ. But maybe you can explain a bit about it.
>Game theory has a host of methods from all over mathematics to prove new results, using new mathematical results derived solely to prove results in game theory. Grab a monograph and see if any of this is deep enough for you.
I'm very familiar with game theory. But thanks for the advice. In return, I'd suggest you read the required reading for the first and second years of a PhD program. Something like graduate Micro and Macro. You might still consider the math deep, but you won't see any category theory or algebraic topology, and existence and uniqueness theorems will be relegated to appendices in fine print.