Why not target business owners who hire illegals?
There are certain limits to this. You don't want to create an environment where employers are terrified to hire anyone. Some kid offers to sweep the store for $10, you say yes, you pay him $10, he turns out to be illegal, and now the feds are shutting down your store.
There's a certain grey area that we don't want to destroy. When I was 12 or 13, I helped paint a friend's business. I was paid $100 cash. It's already illegal to do this, but the punishment is mild enough to allow some things to happen. Kids can make some money under the table without threatening the future of a business. This is the law employers currently deal with. They hire some illegal guys, pay them cash, and that's it. They work in a way similar to independent contractors. If you try to come down hard on businesses that hire people without paperwork, it's going to have a lot of very negative side effects. Sweeping a floor for $10 is never going to happen. Helping a friend paint his store is never going to happen.
We give Trump a lot of shit for creating fear and regime uncertainty, and coming down on business would make this a lot worse. People need to be checked at other times. A lot of criminals are captured when pulled over for traffic stops, and that could apply to illegal immigrants too. If people are working under the table and they never get pulled over or break any laws or need to present ID, I can't really say shit about them. If they're not bothering anyone, why rush to kick them out?