I suspect it has a lot to do with the rise of relatively cheap global travel and strong disparity in the median wealth of different nations. 100+ years ago could you travel from a poor country to a wealthy country with relative ease and expect to raise your own standard of living? Either the journey was expensive and arduous, or the situation in places you could travel to was not likely to be a massive improvement on your own. There are very strong exceptions of course; Irish people leaving the famine come to mind, but it pretty much came to people dying to push them to make the trip.
Also, 100+ years ago an immigrant was less likely to be viewed as a burden, because there were fewer (if any) government supports for regular citizens. I'm pretty left politically, but I acknowledge that the more government spends on its people the less likely the government (and the voters) are to be inclined to let newcomers in who are not immediate contributors.
States in the US have different laws (consider income tax rates), and travel inside the US is super cheap, but we don't see people migrating like crazy to avoid taxes or get free stuff from the government.
I think "to avoid taxes or get free stuff from the government" was an essential condition on what you just quoted. And for what it's worth I think I agree -- I don't think I know anyone who has moved to a state mainly for tax reasons. (Though I do know people who have avoided moving to California, allegedly because of taxes.)
Though maybe the fact that people can move to take advantage of state giveaways, is a big constraint on the way they're currently designed? What conditions does Alaska put on its Permanent Fund payments?
People change states all the time, and generally for reasons you might think. It's not so much "I want to lower my tax burden" but "my paycheck will be higher and my housing costs lower - and the schools are better!", which of course is often related to tax policy.
I beg to differ with your last argument, France and USA have really different approach in how they support citizens, yet both are currently really opposed to let newcomers enter their borders.
I think one problem is like you said, the huge improvement in ones' situation when moving to a new country.
Why is there such a big difference ? Why money is concentrated in so little space and groups of people?
France and the US, while different, both offer far better supports to their people than most of the world enjoys. Social security, free public schooling (admittedly of dubious quality), physical security, etc.
Another issue, I suppose, is that if you've built yourself a population-stable enclave where the prevailing values match those you think are best, you will be understandably hesitant at permitting large influxes of people with different value systems.
For instance, say you've built a society that is ecologically sustainable and the birth rate is equal to the maintenance rate. Will you be pleased when the nation next door where people have far more children despite knowing the Earth is well over carrying capacity sends you its people during famine?
A hundred years ago it was much more expensive to travel, and governments less forgiving about cultural differences when enforcing local laws against immigrants. That doesn't mean it would be a sane policy today.
To put it another way, would you be okay with the entire Chinese army "immigrating" in preparation for an attack, as long as they all represented themselves as private citizens during the trip?
If not, then you agree with immigration restrictions in principle, "and we're just haggling over the price".
Nowadays, travel is much more efficient. Therefore, we have to artificially make it difficult, otherwise large migrations will occur.
Suppose you are on a ship carrying a thousand people. If all people want to go to the left side then there's a big chance the ship will sink. Passengers are free but there must be some limitations to what they can all decide on total.
It never occurred to me that the world was like this as recently as 100 years ago!