Pick one of two: free immigration or a welfare state

As we all know Uncle Milt told us that we could have either a welfare state or free immigration. We can't have both: for we'll attract an awful lot of immigrants with a generous welfare state. Bryan Caplan presents a little chart that shows another, supporting, reason for this:


There's a correlation there between places that are racially mixed (yes, I know, human "races" is a misnomer, think of tribes, cultural backgrounds, whatever, but race is a reasonable enough word with that caveat) and having a low welfare state. The thinking is that people are happy enough to build a safety net for "people like us" whoever that us happens to be. But not so keen on putting hands in pockets (or having the State's hands in our pockets) for those who are the other. Thus culturally homogenous places seem happy enough to have large welfare states, societies that aren't not so much.

Which leads us to an interesting place: it's quite obvious that the greatest increase in human flourishing and wealth comes from an open immigration policy rather than a large and all encompassing welfare state. We can move an Ethiopian taxi driver from an income of a couple of thousand $ a year to $30,000 a year just by moving him to New York City. That's something that almost no welfare state could manage. No politically achievable one at least.

So, if we cannot have both a welfare state and also free immigration, but free immigration improves the general human lot more than a welfare state, then shouldn't we get rid of the one we currently have and pick up the one we don't? Have free immigration and not the welfare state?