Oatmeal Agitante

Instantiating the halting prob. can be how you *prove* undecidability in probs of interest for other reasons; I've seen that.

in those cases I always feel let down because the halting problem usually isn't a "pragmatic" usage of a system

yes, not all sentences in first-order logic are decidable, but I'm not interested in using any old sentence, just useful ones

This line of reasoning seems wrong to me. Do you have reason to think you're interested in a subclass that's decidable?

I suspect not; so it should at least be reason to think you *may* run into undecidability. You seem to disagree.

I'd say that I often have good reason to believe I won't run into the kind of construction the halting problem's proof uses

so, I'm trying to gain intuition for if there's a way for undecidability to "creep up on you"

I think so, but maybe not in problems you work on.