I think the movement of both people, good and capital should be regulated.
The US of the early 1800s was an outlier which has few lessons for today's world.
It had no welfare system to speak of. Immigrants were not a cost to society. There was no extensive educational programs, health care systems or unemployment benefits.
The US was an underpopulated country with vast tracts of land. When the largest farms is Norway was around 20 acres, they gave away 320 acres for free to immigrants in the US. That says something about how insane amounts of land was there.
Thus the US had a shortage of labour relative to resorces. Every person the US got in could work more land and increase the economy.
That is no longer the case. We live in a knowledge economy world where the ability to generate value is strongly tied to your skills and training. Every newcommer is not an immediate asset today the way they were in the 1800s.