Not really, no. That’s mostly propaganda that got pushed hard in the 60s - right around the time the wealth gap really started growing and hasn’t stopped ever since.
The only reasonable argument for any immigration is if it equally enriches all us citizens. Given the ever increasing wealth gap this is obviously not the case.
The alternative is: no immigration, focus on increasing native births by ensuring it’s easy to have a large family. Ensure our elites have a sense of “noblesse oblige” and are self sacrificing instead of chasing profit. Some minor level of immigration is fine (for the Werner von Braun types), but staffing companies that build iPhones and gambling websites is not a good use of our resources.
All of my immigrant friends mention they’ll return to their home country if things get bad here. This is my home country, and I want my country filled with people who are here because they see it as their home, not a business transaction. I have nowhere else to go.