> I suspect if Europe imported more peaceful immigrants, or even had a credible plan to handle this issue, the sudden influx would be less of a problem.
Well, that's the problem, isn't it? If the immigrants are all "some Indian or Russian working at a bank, doing yoga after work and then going home" then we're fine, but unrestricted immigration would mean accepting the violent criminals, or racists, or foreign agents under orders to move to strategic voting districts etc.
> From what I can tell, neither BI nor traditional welfare states can come even remotely close to the benefits of open borders.
Open borders make competition much more aggressive. A complete lack of competition is inefficient, but competition within borders is generally adequate for that, especially when the border is the size of the US or the EU.
Sufficiently aggressive competition produces local maxima. It means no one has any margins to invest in the future. It erodes the tax base because taxes have to come only out of discretionary income or people will starve, but with enough competition employers can pay subsistence wages. And consumers making subsistence wages are price sensitive which drives down the margins of businesses. This is all very "efficient" -- it's the thing competition is "good at" -- except that it means there is no money for people to go to college or do any R&D that won't pay out in the current fiscal year or anything like that.
Borders artificially reduce competition somewhat. That isn't always bad.
A basic income helps with this. It gives people unconditional money that they can use to escape the local maxima created by aggressively competitive markets. Then those people can go to college and invent medicines and technologies that benefit people on the other side of the border.
That works better than everyone being "equal" because everyone is making subsistence wages.