Immigration isn't a binary decision for a state. Its a complex set of policy decisions. What is the state of the local economy? What skills do the new immigrants have? How much experience does the local population have with the incoming culture? What is the culture of the incoming migrants? All of these and many other things comes into play when evaluating or deciding upon immigration policies. For example, taking in Catholics from northern Mexico is nothing like taking in people from the tribals of Pakistan. Most European (quite naive) immigration policies from 10 years ago seemed so poorly thought out that they were doomed to fail. The swing the other way seems guaranteed based upon how bad those previous policies were.

PS The US does it well in general but there were periods of madness recently. The political discourse of many still shows extreme madness is still possible.

PPS The very wealthy are normally the main beneficiaries of immigration and undocumented immigration just creates an underclass with few to no legal protections.