For example, I've heard from a small but non-trivial number of swing supporters that they would have voted for Sanders, but instead voted for Trump. Ranked voting might have allowed them to vote Sanders > Trump > Hillary in 2016. Others may have preferred Rand Paul, or Gary Johnson, etc.
FPTP is directly responsible for our dichotomous and increasingly unstable political system. We need more choice at the ballot box.
If there's a sizeable proportion of people like that, they'd be able to get their candidate in the primary. By and large you need far fewer votes to win the primary than to win the general.
It always surprises me that there are people who don't bother to vote in the first round of voting, and then complain about the quality of candidates that made it to the second round. Well, yeah; you can't sit things out and hope that other people will pick the person you like. Only 28.5% of eligible voters voted in the presidential primary in 2016 (and non-presidential primaries often have lower turnout).
This was the focus of my post, though I guess it wasn't clear...
What you're suggesting doesn't work across party lines. The Democrat primaries don't care whether Republicans would have voted for Sanders over Trump, and the Republican primaries have a similar problem. Primary systems acts to amplify the passionate voices within each party at the cost of bipartisan preferences.