For a limited number of positions, if you have a bigger pool of people to hire from, the wages will automatically go down. This is simple economics.
While the union effect might also be playing a role, it's curious that you rush to deny the big obvious factor while propping up a relatively minor reasoning factor as a primary one.
Probably because it seems doubtful that ten million people (the estimated number of illegal aliens in the US), tanked wages for everyone in a country of 330 million.
It's curious you immediately point to illegal immigration as the big obvious factor with no citations to support your claims.
The fact is wages have been stagnating since the seventies and most people attribute that to the weakening of unions, offshoring, and automation before illegal immigration.
The US is producing twice as much today as it was in 1984 with a third less workers. That seems like it'd have a much bigger impact to me. And painting immigrants as the reason American's qualities of life has dropped off seems disingenuous, simplistic, and prejudiced.
While the union effect might also be playing a role, it's curious that you rush to deny the big obvious factor while propping up a relatively minor reasoning factor as a primary one.