J.D Vance is correct when it comes to the relationship between wages and the supply of labor.

Immigrants increase the supply of labor, which drives down the bargaining power of the individual and increases the power of corporations. This leads to wage stagnation, the destruction of unions, lower long-term productivity growth rates, and record high corporate profits. It’s no accident that both parties have supported mass immigration over the past 50 years, the corporate donors love it.

So you are wrong to say that less immigrants would have zero economic impact on the socioeconomic well-being of Appalachia. It absolutely would.