Certainly there are places like the UK, or my homeland, Canada, that have had three relevant parties for a while without changing the system. Although both UK and Canada have forces pushing for reform. The recently elected government of Canada gave an election promise to change the system, but, well, I'm not holding my breath.

But I'm not saying at all that any country with multiple parties will enact voting reform, but statistically, it seems that voting reform is often brought about that way.

I suspect IRV was brought to vote in the UK, because that was deal that could be reached between the Conservatives who didn't want change, and the Liberal Democrats who did. However, I will note that IRV isn't so bad when selecting members of a legislature. Approval/Condorcet elect compromise candidates, but we don't want to simply have a legislature of compromise candidates, but rather representative of how people voted. But some from of proportional system is probably better.