"Then there's of course the fact that almost nobody (with citizenship) actually wants to pick crops, no matter what you pay them, because it's back-breaking labor. "
This is not true. There is absolutely a pay rate, and set of labour conditions in which Americans will do those jobs.
There are tons of innovation in labour: grabber/chopper rods so that people don't have to bend over all day - for example, could be one such innovation. But maybe it cuts down productivity by 30% - so in a 'cheap labour' world it would never be conceived of.
But if labour costs are high, and farm workers have to actually pay Americans - then guess what - those types of innovations definitely happen.
Do you realize how many 'really crap' jobs there are out there?
How about dealing with screaming customers all day on the phone, trying to 'upsell' them?
Some people prefer not dealing with issues, and doing something repetitive.
Also - the hypocrisy of employers not paying for social services, healthcare, taxes - etc. etc. - but the government giving them social services and 'access to emergency healthcare' and drivers licences?
Basically, farmers are externalizing the social costs of their labour onto you and I, in an inefficient way.
This is totally wrong.
Farmers - and others - are pushed to use 'illegal labour' because if 'the farmer next door' is doing it, and the 'farmer down the street is' - then they have no choice to.
The best thing is to make sure that everyone is paying minimum wage, taxes, basic healthcare, respecting workplace regulations etc. - and even hiring authorized workers.
This means that prices will rise for some things - and you and I will pay more for them in the store - but it's a far more responsible form of capitalism - and prices more accurately reflect cost to society.
Some things won't be able to be done in the US - that's fine. Move that to other places. Let Mexico and Africa have a cut of the business.
Finally - one way to accommodate a tight labour market in a legal and 'above bar' manner would be to allow for 'pink cards' - i.e. foreign workers can apply for 'pink cards' for specific intervals, they 'check in' and 'check out' of the country given that pink card. That card comes with a 'temp SID' which they can use to pay their taxes, and claim benefits associated with the term.
Unregulated black market economies are good for nobody in the long run, they lead to all sorts of problems and growing inequality.
Enforce immigration and workers laws, provide some ability to help with a tightened labour force (i.e. pink cards) and facilitate good trade flow (i.e. customs unions and free trade) for items which cannot be produced in the US.
"you don't give a shit about people and treat the world solely as an economics textbook"
Trust me - migrant workers 'don't get given a shit about' by anyone, because if they are 'off the books' they have absolutely no protections - nothing.
Put the economy 'above bar'.
There would be no war over migration if we just had some basic but intelligent rules that were responsibly enforced.