It's amazing to me how ingrained the notion that having an illegal workforce is somehow something we just have to accept.

It's not something we have to accept.

But there are real world trade-offs here that can't just be wished away. Any functioning free market economy is going to create very powerful incentives for labor to be used efficiently. That means that workers with a high school education or higher (like nearly all U.S. citizens) are not going to ever efficiently work as field hands for any wage that an agricultural producer can pay.

You can't have both. Low-educated unskilled workers are a necessary factor of production for certain types of agricultural products. You can't have domestic agricultural production for labor-intensive food and prevent the flow international of low-educated unskilled workers.

So - you don't have to bring in those low-educated unskilled workers illegally. You can set up programs where they can come in and work on a temporary basis (like the old bracero programs). Or you can allow enough legal immigration that you have a steady supply of low-educated unskilled folks to serve as farm hands. Or you can allow those segments of domestic agriculture (and other fields that require low-educated unskilled labor) to disappear.

But you don't get to wish away economic realities because they are inconsistent with one's worldview on immigration. If you don't import a necessary factor of production for an industry, and you don't have it domestically, you don't get to have that industry in your country.