In response to (2), most would-be immigrants dream of entering the US with the intent of picking up work, and to be politically feasible in the US, the BJ would have to offer higher (PPP-adjusted) wages in better working conditions than most people expect in the developing world. BJ jobs would be very attractive to most would-be immigrants.

Since BJ labour generally provides less value per hour of work to taxpayers than it costs them to pay for the programme, taxpayers will still want the programme to be as small as possible, which means it's still going to be politically unfeasible to get much closer to open borders.