The United States itself had "open borders" for a long period of time. There was mass immigration from Ireland, Italy, and many other places and it worked out quite well for us.

Even today, we have "open borders" within the US. People are free to move from from poor (or poorly run) communities to places with more opportunities and it's a win-win.

Similarly Europe has 26 countries in the Shengen area. Some of the countries have a "better-than-average standard of living" and they're doing just fine.