The only result of this would be Government looking the other way when their preferred people were hiring illegals. For example, using and gaming the system for political purposes. But there is a more basic reason it won't work.
What you propose is to legislate "black markets" out of existence. In the entire history of man, that has never worked. It has not even worked when the penalty was beheading for those caught.
I am only talking about illegals not black markets. They will always exist. For one reason. They are black. lol.
They have imposed fines on people but it doesnt seem to work as most people who hire illegals could care less. Just give a reason to care a little more and they would stop what they are doing.
Why wouldn't it work? Its a simple process. The way the laws are today there are loads of law enforcement agencies that would jump on this shit. They have no issue jumping on other low rated topics. This would give them something else to do.
It wouldn't stop any black market besides importing illegals for work. If anything it may turn them into slaves.
And now I do not want to hear anything about slavery. As even Jesus had slaves. not that I am religious. Just think its funny how so many Christians think slavery is bad but yet the one they look to and prey to and talk to had slaves.
The whole point is. Not to make it harder for people to employ illegals but to make it so people do not want to. Give them reason not to. Make sense.
Sure, you could do something like this by eliminated cash, then tracking every penny spent by every citizen and business. You'd need to issue to all "Legals" a government cash card for their electronic transactions, and you'd need to outlaw bitcoin, and jail people who used any foreign currencies.
All this would create problems because all of the Congressmen and Senators have workers like Phillipino Maids, who are paid in cash.
So they'd never allow it.