Many people will do the hardest or grossest of jobs if the pay is very good.
Look no further than skilled medicine. Podiatry and Proctology pay a lot better than the less-gross specialities. Everybody has their price in a society. If you're willing to create a large social safety net and under-bid the value of labor by importing the third world, every single job will be done for less because you've lowered the prevailing market wage.
A perfect example is the stereotype of residential roofers. In most areas, they are stormchasers of Hondurans and other central Americans. They largely displaced illegal Mexicans and Caucasian citizens with criminal records. The prices are so low, you cannot find legal, employable people to do the work. But what about commercial union roofers? Yeah, they have to be bonded, insured, and legal. Their wages are six-figure because of the barrier against illegal workers.
So, who is at fault here, the Mexican, Central or South American, or the local roofing company who is hiring these illegals, and paying them way below what the minimum pay should be for a roofer? Now, here where I live in GA, without them, it would be almost impossible to build a house. If burger flippers are demanding $20+ an hour, how much would a roofer, carpenter, brick layer should be paid?
There are ways to get good workers to do the job no one wants to do. Lane's here where I live have been doing it for years. They come in with their workers visa, they do their work, and after 11 months or so, they go home, to come back later. But some companies do not want to go through the hassle and hire the first one that comes along. If there were no "Illegal jobs" to be offered, we wouldn't have this issue.
When my mom immigrated into the US back in 1968, she was given a job to do (building mother boards for radios) with her green card, she didn't have a choice, she had to take the job if she wanted to come into the US. She didn't come to the US to become a parasite of the system, like we see now a days. God forbid if we did that now, what would that be call?
When I joined the military in 1983, I cleaned latrines, waxed the floors, used razor blades to remove excess wax from the floors, pickup cigarettes butts, mowed the lawn around the building I worked at, washed and waxed the General's car, and who knows what other manual labor I did. Try to do that with our new military. It's not going to happen. But now we pay contractors to do the work we did.
So, again, who is to blame here? Unfortunately, it's our system.