This argument is a bit double-edged. Okay, so it's implicitly immoral to keep immigrants out. But it's moral to hire them for jobs that Americans won't do because they're so unpleasant?
At the same time, I think we should make an effort to ensure people are doing it legally and benefit from the same worker protections that make hiring citizens so expensive. And we should crack down on people who hire undocumented workers or off the books employees.
I think if we did that, it would dramatically cut down on immigration without imposing quotas because there won't be huge numbers of jobs for unskilled workers making slave wages.
Farmers that want to do that will have to move their operations to Mexico or some other country with lax labor laws.
What makes it 'unpleasant' is the destruction of the social contract that valued 'regular work', and the fulfillment of specific jobs by illegal migrants which creates a negative 'social class signalling' dynamic to the work.
It's socially destructive, and irreversible - and I believe it adds considerably to inequality.
And yeah, some of the jobs are very unpleasant (I've worked a few of them). The article's sly portrayal of toothless guys and drug addicts refusing cushy gigs picking grapes at vineyards is meant to give an impression without coming out and saying something that probably cannot be supported by the data: the jobs are good and the citizens are lazy.
Every argument that "we simply can't get American citizens to do it" seems to be an appeal to a broken system staying broken.