You can call someone's reasoning circular all you want but at the end of the day there's what you've accomplished, and the score is philospher 0 engineer 1.
True, it's basically indisputable that engineers are better at engineering than philosophers are. But that seems orthogonal to the issues raised in the problem of induction.
My thrust was more that people are out doing stuff in the world, and for the most part philosophers don't do anything other than say things about what people are already doing. Engineering was an empirical science long before it was a deductive and analytic one.
Philosophers make arguments for/against claims, I don't see why that doesn't count as doing something. I mean, maybe you're complaining that they're not building rockets or feeding the poor, but philosophers are far from the only ones who don't do these things.
But Popper wasn't saying that empiricism could be justified empirically, was he?
In his own words, in the section on the problem of induction in The Logic of Scientific Discovery:
"My own view is that the various difficulties of inductive logic here
sketched are insurmountable. So also, I fear, are those inherent in the
doctrine, so widely current today, that inductive inference, although
not ‘strictly valid’, can attain some degree of ‘reliability’ or of ‘probability’."
He then goes on to provide the (now contentious) falsification-based view of science after conceding that inductivism can't work.