I don't know your family, obviously, but my prior probability is that migration to America would be an incentive, not a deterrent. The reason bringing relatives from 3rd world countries is such an studied problem is that so many people want to come here.
I think your prior is off...not to mention that if they wanted to, they would have done it long ago.
In my experience, immigrants are a rather unusual group of humans with a unique personality profile - most people wouldn't voluntarily move to a new place where they don't know anyone.
(If you don't think it is that unusual to be willing to move, do keep in mind that America's culture is unusually individualistic.)
Among those who would leave their homeland, America has been a popular destination...but most people wouldn't leave their homeland.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.