This is a problem also illustrated by Israel.
If Israel grants "The right of return" to people displaced by the creation of the "Jewish" state then Israel will cease to exist.
If the US and Australia and to a lesser degree Canada opens their borders will they cease to exist as a viable republican democracy?
Personally I don't think so as most of the people wishing to enter the aforementioned "nations" generally wish to emulate the conditions found there. The Palestinians officially deny Israels right to exist at all. This does not seem to be a problem with either the Central American of the Southeast Asian emmigrants.
Any company is duty bound to make its manufactures as inexpensive as possible to its customers. If Americans and Australians cannot work as efficiently as Mexicans and Asians this is more the fault of the employees and managers than the immigrants.
Nationalism rears its ugly head occasionally. Adam Smith will ensure that its macabre grin will eventually be wiped off. And Mexico and South East Asia's governers will eventually be supplanted by ones more responsive to the needs and aspirations of their citizens.
I'd bet on it but I won't hold my breath while I wait for it to happen. Meanwhile it behooves us not to add to the worlds miseries.
Sorry if I talk to much. Some problems just don't have easy answers.