I cannot think of any Republican politician in Appalachia who would be a member of a left-wing party in Europe. It is true that there are at least parts of Appalachia that, if transported to Europe, would plausibly vote for the left, but that's different.
Yes, one of the mistakes people make in these threads is to assume that
the same people would be in politics and successful at it in the hypothetical scenario, when actually the biggest difference between these things in different countries is often the sort of people who actually get elected. You won't find many politicians with a background as an estate agent in the average European country; conversely, Congress is not exactly filled with people who used to have political or administrative posts with major Trade Unions.