I agree that doing something useful is more important than doing something scientific. (I assume you left out the negation in that sentence.) Of course, scientific status is supposed to indicate maximal cognitive utility.

I don't think I write anywhere, as you say, that "a model should be so simplistic that it no longer does justice to what's being explained." (Again, did you leave out the negation?) What I say is that models inevitably simplify, but they shouldn't oversimplify or distort the facts. Arguably, some fundamental economic models do the latter rather than the former.

There are many applications of economics, but a technological application would be a greater confirmation of the field's models. Having an economist on the payroll is far from having a technological application since economists might be there for show or because managers have been hoodwinked by a pseudoscience.

No, what I find suspicious is the lack of technological applications together with the alleged mathematical rigor of economic models. If your knowledge is that precise, why are there still gaping holes in your predictions, and why can't you use that knowledge to control economies or to exploit economic forces? The reason economists can't is that social phenomena aren't so predictable, which means the economisit's dazzling math is itself for show.

You ask a good pragmatic question at the end there. My answer is that I criticize economics because of the harm it's done in cheerleading for a runaway form of capitalism. If economics isn't as scientific as economists maintain, their professional advice carries less weight, which means we shouldn't defer to it.