The more you think about it the worse it gets. It's one thing to be in favor of immigration, it's another thing entirely to be in favor of illegal immigration. The Tyson Chickens of the world love illegal immigrants, they don't file workers comp claims or take you to court if you fail to pay them. Supporting illegal immigration is supporting the creation of a untouchable quasi-slave caste. If immigrants had the same rights, privileges and responsibilities of domestic workers, they probably wouldn't work for such a steep discount. This is why I believe many proported immigration proponents don't ever seem to manage to meaningfully open up the border, that isn't what they are going for.
That's certainly right. One of the big lies in the US today about illegal immigration is that there are 11 million illegal immigrants in the US. That has been the same number touted for most of two decades (it's still mindlessly repeated by talking heads on TV).
The real number is now closer to 22 million illegal immigrants, according to a recent Yale study [1]. Representing around 6% of all people in the US. So wait, how are all of those people surviving? They're cheap labor for the big business machine, they're an unprotected cheap labor caste as you correctly point out. They can't complain, they don't have well protected worker rights, and it can take a long time to become a citizen. It's a human rights travesty, and both the big business conservatives and the Democrats (as both are pro open borders) are morally culpable for it.
The rational approach for the US would be to remodel its immigration system as something similar to Canada, focused more on high skill labor. We need to turn off the flood of illegal immigration while simultaneously creating a reasonable citizenship pathway for the 22 million illegal immigrants that are here now (most are never leaving, so the proper thing to do is to provide a citizenship pathway), which would also begin bringing them into the tax base and protecting them as workers.
Or simply relax immigration policies to basically let migrants get work permits, they would argue for a fair wage, and we can let the market decide. From what history says, that's what the US used to be in previous centuries. People came and worked, and grew and made what the US had become before politicians decided to make it harder and harder for migrants to settle legally.