I wholeheartedly object to this line of thinking.
The reason most US citizens have shunned these jobs is because the wages paid are so unreasonably low because the labor market wages are dictated by the wage demands. And that wage demand is greatly driven DOWN by the presence of illegal immigrants who are willing to work for much less than what is deemed a "livable" wage by US citizens.
This isn't an argument for a more immigration, but against. There is work that needs to go back to legal US citizens, but they will not subject themselves to live off of the paltry wages that employers pay the illegal immigrants. There are a lot of US citizens who would be willing to do this work, but are priced out by the companies that hire illegal immigrants.
And how do other countries possibly get all of this "undesirable" work done without non-citizens outside of the bounds of their laws? How on earth does Germany function without a slew of illegal Slavic immigrants to do their landscaping and fruit harvesting? How does Japan do it without a bunch of illegal Koreans to work in their poultry factories?
My point is they do just fine and we would too if employers weren't accustomed to the below market wages of illegal immigrants.