When the national elections are still two party local, and the two big parties have any interest in the local election, those two parties will win local as well because they have some much more mind share. Many people decide who to vote for in the national election and then vote the same party all down the ballot without knowing what any of the other players stand for, thus giving the major parties a big advantage when one of those down ballot races is a different system. If you are not the big party in those other systems you still have a harder time because people don't understand how the local system is different.
Again, I ask, where has this two-party to multiparty switch happened with single member elections?
Because I can't find an example in any country, yet it is appears to be taken as an article of faith that it will happen by proponents of ranked choice voting.
The evidence for switching from single member to multi-member elections is far more clear. Of course, you obviously can't have multi-member elections for President, the Senate because the Constitution staggered elections and courts have ruled against multi-member districts for the House in the past for violating the VRA.
I'm not aware of enough world politics to tell you if it has happened. I would not expect such a change to happen overnight, instead it would take 50-100 years for people to get used to the change and then change how they act. Thus a lack of any examples doesn't mean it won't happen. (it also doesn't mean it will - politics are always changing)
It hasn't happened anywhere in the US as far as I know, despite being adopted by various local governments.
Ranked choice's major benefit is that it reduces the effect of spoilers. Third parties are the spoilers.