I'm not sure what you're describing. As long as one of the top two candidates appear on your ballot (at any rank) then you have influenced the last round of voting.
45% of voters rank A 1st, B 2nd, C 3rd
25% of voters rank B 1st, A 2nd, C 3rd
30% of voters rank C 1st, B 2nd, A 3rd
Nobody has the majority, so B is eliminated, and A wins round 2 with 70%. But 30% of voters preferred B over A, and if they had ranked B first, then B would've won in the first round with 55%. By voting honestly, the C voters threw away their votes. None of their later rankings mattered, because C was not eliminated before a victor was declared.
But suppose you're right and voters rank candidates honestly because they can't predict how to vote strategically; ultimately, I think that is arguably even worse, because even if voters can't predict how to vote strategically in advance, they can certainly still feel resentful after the fact when the results are tallied and it becomes clear that they got screwed over by voting honestly. At least in plurality voting, it's easy to understand the tradeoffs and choose whether you want to vote for a spoiler candidate or not. Surely it will not lead to greater voter enfranchisement for people who find out after they voted that they accidentally spoiled their own votes, and could've had a say in the outcome if they'd expressed their rankings differently.
If this still all sounds hypothetical, keep in mind that this is exactly what happened in the 2009 Burlington, VT mayoral election. The Republican candidate acted as a spoiler for the Democrat (who had the broadest popular support) and instead the Democrat was eliminated and the third-party Progressive candidate was elected. This led to wide-spread dissatisfaction and IRV was repealed there in 2010.
45% of voters rank Trump 1st, Romney 2nd, Biden 3rd
25% of voters rank Romney 1st, Trump 2nd, Biden 3rd
30% of voters rank Biden 1st, Romney 2nd, Trump 3rd
This seems like a fairly plausible real-world situation, and it also seems pretty easy to imagine how Democrats could look at the polling numbers and realize that Biden is never going to win in their state, and that ranking Romney 1st is their only chance to stop Trump.