I'm not sure this is actually capturing the heart of the current arguments from current U.S. citizens, which IMO boil down to "how much control over the supply

I'm not sure this is actually capturing the heart of the current arguments from current U.S. citizens, which IMO boil down to "how much control over the supply of labor in the U.S. do U.S. citizens have?" Even if your #1 is true, it doesn't mean that the economic benefits of immigration are distributed in a way that is favorable to the median worker.