Maybe a better way of phrasing what I'm trying to point out is that induction is isolated to a single step. Instead of working directly with probabilities which require a theory of what probabilities are, NHST waves it's hands a bit and treats the inductive step as deductive, but transparently so (once you lay out the deduction anyway).

Your point about a test statistic that's low-probability on all possible model hypotheses is a good one - and it suggests that the details of hypothesis testing should change even if the general logic is kept. I doubt that the details of actually used hypothesis testing are ideal for "induction-free induction" (which I'm realizing is a bad name for what I'm trying to convey), but what I'm really talking about is the general logic. I'd be surprised if some of the details didn't have to change.

I don't think I disagree with anything in your comment though. I don't think I have a strong argument for using hypothesis testing, but it may be that the general logic can be salvaged for a reasonable method of doing induction without fully fleshing out an inductive theory (this is why I said one step requires hand waving).