Good thoughts here.
I never understood the induction bruhaha. Well, I guess I do. But it always seemed to be the result of people worrying about things that weren't worth worrying about.
Induction can be very helpful for understanding things. So use it to understand things. Make sure you are conscious of the fact that it is not a guarantee, and you're golden.
I've always thought about inductive and deductive reasoning in a production function sense too. For epistemological reasons, economists often take a deductive approach. That's fine. Deductive reasoning is a good thing. But we rely so heavily on it its marginal product has to be diminishing by now, and induction has to be worth giving a shot more often than not.