Maybe, but the cost of living in Europe is already considerably higher than in the US (barring of course the popular but disingenuous comparisons between SF/NYC and rural Europe). I'm not an economist, but I wouldn't expect an influx of Americans to drive up the cost of anything except perhaps real estate. Moreover, I wouldn't expect a significant influx of Americans period--relocating to Europe would only be for the intersection of the very privileged, those interested in Europe, and those who have the flexibility to make the move. I'm sure there's some threshold at which too many people are visiting and it's causing problems; however, I'm only arguing that the current state is suboptimal for everyone (although someone else has pointed out that it may be easier to work remotely in Europe than I'm aware of).