While that's a nice sentiment that I agree with, you need to remember that those low paying jobs illegal immigrants often take, still pay far more than they could ever hope to make back home. Add to the low to nonexistent job skills and language issues, they start from far, far behind the eightball.
Having worked with large number of illegals back in the day, I found the vast majority to be quite genuinely nice people and co-workers. And they were some of the hardest workin' sumbitches you would ever be around.
What I found interesting was the friction between the second and younger generations of Tex/Mex families and the newly arrived Mexicans, (I use Mexican to denote the actual country of origin here - sad that I need to do so). The first generation immigrants were very religious and conservative. While the second generations often adopted the more liberal attitudes of the locals. It caused a lot of ill undercurrents between the two groups.
ok, but we can't just let people be underpaid because it's more than people make in, and excuse me for using this term, third world shithole that barely has water infrastructure (I'm looking at you Serbia).
Sadly, it's a chicken and egg situation. You can't get a better job because you have no skills employers will pay more for. And you can't very easily find a way to get those skills because you would get deported because you are somewhere illegally.
It makes for a complicated problem to solve. And I don't have an answer other than to say that it's on the first generation to make it so the following generations climb the ladder upwards.