I agree with everything you said up to "Then hammer the hell out of business that employ people here illegally." I strongly disagree with that.I understand this guy is a tool that has zero comprehension of the history of our country especially when it comes to immigration.
We need to make it easier not harder to come to this country. Ellis island screened people to make sure they didn't have disease or weren't raving lunatics. It wasn't by the way the only Port of entry to the US. People back then simply walked across the border as well
Make it easier for the current immigrants to come and be productive members of society. Then hammer the hell out of business that employ people here illegally...because there would be zero reason for a person to be here illegally that wants to be here legally. If needed make a work visa that participates in things like taxes but allows for a contract on wages to do things like harvest at lower than minimum wage. If that is actually needed.
It should never be illegal to hire someone to do legal work. It should only be illegal to exploit and abuse them, or if they are being hired as part of unscrupulous efforts to break up legal labor activity (such as hiring scabs to break up strikes or disrupt organizing).