US was prosperous post war because the industrial capacity of the rest of the world was destroyed. Comparing that time period to any other doesnt make sense.
We can only employ natives if we want, we just have to accept that prices of things that are currently run on immigrant labor will go up, and a lot less of it will be produced. Personally I am unwilling to make that tradeoff but obviously you dont have to agree. US labor market suffers seriously from baumol's cost disease, only solution to that is immigration with the understanding that immigrants will take unwanted jobs in exchange for a better life for their kids.
Everyone has their own priorities, I guess. I'm not willing to drive down Americans' wages to save a buck on strawberries.