Europe is not Americanizing because the right-wing in Europe still supports the welfare state (at least domestically). If they didn't, they'd get destroyed.
Republicans seem to support the welfare state, to some extent.
In both the US and Europe, conservatives only support maintaining the welfare up to the point it is already established. They always oppose expanding it.
Of course, in Europe, it has been expanded much more. That's why European conservatives appear less conservative than their American counterparts.
Really though, if they both had a free hand, they would both dismantle their welfare states completely.