I think you make excellent points. I think where we'd probably disagree is in how quickly (or easily) we'd reach some sort of equillibrium state.
You are absolutely right that countries which enjoy greater public benefits would likely enjoy a greater influx of people. But I disagree that that's necessarily a bad thing. I'm a firm believer that there is no such thing as a free lunch. And if residents of Iceland make it so appealing to just live there without contributing to society, then I don't see how it is a (globally-speaking) bad thing to have migration make it so that enough people decide to move there to make it less feasible.
Let's not forget: The people supposedly moving into those economies would likely be fleeing oppressive regimes with very little economic opportunities. And, with free movement, it would become much harder to give away freebies, AS it would become much harder to become an oppressive government. Stories like Venezuela would be more hard to come by if people could simply leave the country more easily.
Just take familiar HN-turf: Software development. What do you think would happen if all Indian developers (many of whom are actually really, really talented), could just as easily apply for jobs in the US? Undoubtedly worse for US-based developers, right? And maybe there is some sense that such a massive disrpution should be avoided, at least "suddenly" as you say.
But now you multiply this across every industry, with all of their individual justifications, and what you end up with is with an ossified global society. We end up trying each to protect our pie (from crop subsidies on out), all perfectly justifiable. But, as a global community, we make it worse for all of us.
Just this week Elon tried to inspire us about the idea of an interplanetary species. It just seems inconsistent to me for us to dream about being a people who can travel freely to the stars, but that we need to ask permissions of random strangers to visit family members, to employ our talent productively far from where we were born, etc.
I think you raise really valid points. But in my eyes, those are issues to be dealt with in the pursuit of this ideal, not justifications on why it should not be pursued/is not feasible.