I don't propose that states automatically grant welfare to any visitors; it's free movement that I claim is a fundamental right, not free money. Nor do I propose immigrants have automatic citizens' votes, not in any immediate time period. Nor that such welfare issues be up for a democratic vote -- they could be a constitutional issue instead.
I don't see how, with these qualifications, this leads to a collapsed welfare state. Without welfare guarantees (at least not for new immigrants), there's no selection tendency for rent-seeking. Instead there's selection pressure for hard-working people, living in states where their efforts are undervalued (because of broken government or broken economy).
On a side note, I believe that immigration discrimination is good. It allows minorities who are productive members of socialist societies (i.e. tax heavy) to flee in to countries where their skills are valued.
I think you've misunderstood your argument. You've argued that permitting highly-skilled immigration is beneficial; but not that restricting low-skilled immigration isn't. What's the economic argument for trade barriers on low-skilled labor?