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Most of the arguments Republicans made after that election were bad.
But that election was genuinely an example of a number of the unfortunate pathological edgecases in ranked choice.
In particular, it failed a number of the mathematical fairness criteria that people have come up with over the years to compare voting systems. Much of it stems from the failure to elect the Condorcet winner, Begich. Basically, Begich could have beaten either Peltola or Palin in a head-to-head election, but he had fewer first place votes than either so he was eliminated first and Peltola beat Palin in the last round.
So first, it failed 'favorite betrayal' - Palin voters would have been better off voting for Begich. It failed participation: if a bunch of Palin voters stayed home, Begich would have won and they'd be better off. It failed monotonicity: Palin voters could have defeated Peltola by voting for her. Obviously, it failed independence of irrelevant alternatives; Palin acted as a spoiler candidate to Begich.
All of which isn't an argument for regular party primaries + plurality, which is theoretically much worse. But it's the example advocates of alternative systems like approval or STAR will reach for for a while, just like Burlington used to be.
That doesn't sound like a failure to me, unless you wanted a Republican representative. And saying "if more people had voted for Palin she would have won" is pretty laughable. All Republicans had to do was vote Palin 1st, Begich 2nd (or vice versa) and they would have then had their pick in the next round, but Palin was such an awful candidate, Begich's supporters would rather see Peltola over her (as they should), and Palin's supporters seemingly didn't vote for Begich either. No matter how you slice it, the Republicans screwed themselves, and I am here for it.
Failures shouldn't be judged by a standard of "this worked in my favor this time so it's good".
This time, it benefitted Democrats. Next time, with a different set of candidates, it could elect someone alt-right when most voters preferred an establishment Democrat.
And Palin definitely shouldn't have won. Most other voting systems would have elected Begich.
The problem is that IRV genuinely has a lot of weird behavior because the results are so tied to elimination order. You can actually see that visually in a kind of election visualizion called a Yee diagram, where you put candidates on a political compass and color the regions that they'd win if the center of opinion is in that region. Most systems produce sensible diagrams, IRV often produces bonkers ones.