After some reflection of what you wrote and what I wrote before I think the problem I was trying to articulate is actually an interesting subset of a more general problem, namely the Halting problem, as it applies to humans.
That is, how does one know when to stop inducing on a chain of inductions? Because surely there has to be a threshold, as with the neutrino example, beyond which induction will most likely yield a misleading answer that if taken at face value like every previous stage of induction, will lead down a garden path. Identifying that threshold every time may indeed be impossible without knowing everything.
Any pattern identified by induction either continues to hold, in which case it is fine to believe it, or it stops holding, in which case it must be adjusted. A generalization is a form of induction, and so acts the same. Could you provide an example of induction leading down a garden path?
I can think immediately of Maxwell’s electromagnetic theory following the previously accepted theory of some ’Luminiferous aether’ which was at the time believed to be what light propagated through in a vacuum. Going from Newton → to ‘Luminiferous aether’ using induction works fine, explains many observable phenomena, and is somewhat elegant too. Compare the next step to Maxwell’s equations which are horrendously baroque and reliant on much more sophisticated math with some really bizarre implications that were difficult to accept until Einstein came along. There doesn’t appear to be any way induction would have led you to the correct result had you been researching this topic in the mid 19th century. In fact many people did waste their lives on the garden path trying to induce onwards from the aether.