I will add my own rough theory here. Since American students are not trained in basic logic, I think that the critical fact is that they have no familiarity or understanding about implication statements $P \Rightarrow Q$. In many cases they'll be learning about the form of an implication statement, as well as induction, all at the same time, and they can't distinguish between the two issues.

If there was more teaching of basic logic, and completely separate exercises on proving implication statements alone, then I would expect the difficulty of induction to be at least somewhat reduced.

I will add my own rough theory here. Since American students are not trained in basic logic, I think the critical fact is that they have no familiarity or understanding about implication statements $P \Rightarrow Q$. In many cases they'll be learning about the form of an implication statement, as well as induction, all at the same time, and they can't distinguish between the two issues.

If there was more teaching of basic logic, and completely separate exercises on proving implication statements alone, then I would expect the difficulty of induction to be at least somewhat reduced.