STAR is basically fine, it's a variant on score.

There are several problems with IRV, but the most obvious one is that it can often knock the moderate candidate out of the final round.

Suppose you have a district that goes 60% for one party. That party runs two candidates and the other party runs one. With IRV, one of the first party's candidates is the most likely to get knocked out, because they'll each average ~30% of the vote (half of 60%) while the other candidate gets the other 40%. But if the majority party then has a preference for their own extremist, it's their moderate that gets knocked out, and then in a district that goes 60% for that party, the extremist has a decent chance of getting in.

The same dynamic can also cause the minority party candidate to win. 51% of the majority party (i.e. 30.5% of the district's voters) prefer an extremist, but enough of the majority party is afraid of them that in combination with the 40% of the vote from the minority party, the minority party wins the run off. Even though the "winner" would have lost to the majority party's moderate using score voting regardless of whether the extremist was on the ballot and even in a two-candidate election using FPTP.