I am not convinced that BI and open borders are incompatible. So a lot of people move to the US - how is that harmful? Historically, increased immigration has lead economic happytimes. It's unlikely to get overcrowded; if the entire population of the world moved to the US we'd still be substantially less crowded than Singapore, and there's no freakin' way that would happen.

If we find that BI has problems, we roll it back. If we find that the only problem with BI is immigration related, we can encourage other countries to implement it too - possibly coupled with aid, if they need it.

I'd want to take a closer look before doing it, but it doesn't seem as crazy as common wisdom would suggest.