I think QED provides a nice example. I don't know if there are any formal mathematical constraints on the size of theoryspace, but for practical purposes we can probably agree that one may conceive of arbitrarily many hypotheses that fail to be falsified by a given set of observations. If deduction is all we have at our disposal, how do we choose among all these options? And should we really not have any more confidence in a theory like QED which as been tested many times and "failed to be falsified" to nine significant digits, versus one that has only "failed to be falsified" at 5% relative?
In practice, I would also claim that parsimony is (and has been historically) absolutely critical in culling away the dross of theoryspace, yet this can hardly be presented as a deductive method?
I think induction has been given an unnecessarily bad name lately. The falsification-centric paradigm that is popular today was proposed by Karl Popper as a solution to Hume's "problem of induction" [1] -- but Hume, and the rest of the Empiricists that laid the foundation for the scientific method, would have considered this entirely backwards. While Hume did claim that induction could not be justified by reason alone, Hume's conclusion was not to reject induction, but rather to prefer induction over deduction!
> It is far better, Hume concludes, to rely on “the ordinary wisdom of nature”, which ensures that we form beliefs “by some instinct or mechanical tendency”, rather than trusting it to “the fallacious deductions of our reason” [2]
[1] https://en.wikipedia.org/wiki/Hume%27s_problem_of_induction