In the case of the United States, most definitely, yes!
The reason why we in the United States are dependent on a steady influx of immigration is that our oligarchic systems have empathy, praise, and respect only for a steep but narrow sliver of people resources, all while the needs of any country needing to continually reinvent and adapt itself are highly dependent on ample supply of outliers on either side.
Meaning, if one would plot out the bell-curve of resources we need as a country from skilled capacity on one side to skilled ingenuity on the other, our oligarchy, deployed by the systems we built, would generally focus on the resources willing and able to conform to the oligarchy, and steadily ignore the vast need for skilled resources on either side of the aforementioned spectrum.
Without a flexible immigration policy, our country would increasingly become more deplete of outliers on either side, the very outliers it prides itself on regenerating. Courtesy of our freedom held hostage by a grandiose lie of oligarchic proportion.
Until we reinvent the systems that determine what we can discover (Einstein) to be in conformance with the principles of renewability and treat our own people with the respect and empathy they deserve, will we be dependent on external human resources derived from immigration to replenish ourselves?