It would create many economical forces causing investors to not want to invest in the stock market, eventually causing its demise. Each one has been already described in other comments.

From my (EU citizen) POI, please go ahead. This will help Europe greatly as it's the most rational place to move assets for most Americans, with many great places with great tax and business culture + these are really nice places to live in, actually. That will in turn raise EU wages to the likes of the USA - thanks!