> If this scenario isn't super weirdly convoluted, more of those votes shift to B than X, so X is eliminated next.

It doesn't have to be that convoluted, all it takes is for the eliminated candidate to be a moderate so their votes go in two different directions. But you're right that I messed up that example; the percentages are wrong.

The problem case is when your second most favored candidate would otherwise be eliminated first and you need to prevent that by causing your most favored candidate to be eliminated instead, because the second best candidate has a better chance in the next round.

Suppose the candidates you dislike, X and Y, are the first choice of 40% and 25% of people respectively, and then A and B split the remainder evenly. X and Y are the two extremists -- on opposite sides of each other, with the moderates A and B in the middle. You favor A but A leans in the direction of X and B leans in the direction of Y.

If B is eliminated first then half of B's support goes A but half goes to Y, Y is still ahead of A and then A is eliminated next. If A -- your preferred candidate -- is eliminated first, half their support goes to B and the other half to X but Y gets nothing. Y then loses to B and the final round is X vs. B rather than X vs. Y. And the elimination of Y puts all their support behind B since X is the opposite extreme. But only if you rank B above A even though that's not what you'd have preferred.

> Yeah that's a real issue, and I'd want to use condorcet methods to fix that.

But now you're no longer using RCV/IRV. Score voting is a Condorcet method.

> Meanwhile with approval or score voting, a lot of people pretend not to like the other party's moderate because they're trying to get their side to win and it gets really messy.

Except that doesn't really help them because doing that also makes it more likely that their least favorite candidate wins, which is a significant incentive not to do it. The only reason to do that is if you're confident your favored candidate could only lose to your second choice, in which case it was really a two candidate race to begin with.

> Is there a need to have multiple candidates per party? If there is, a two stage election that picks party first and then picks probably-the-moderate is probably better than anything.

It doesn't matter if they're in the same party or not. If you're using a voting system that allows more than two parties to be viable then you'll have similar candidates running from similar parties. "Force the election to be one candidate from each of two major parties" is FPTP and it's terrible.