By the logic of capitalism the way to eliminate every undocumented migrant worker's job is to (a) remove ICE as a threat that bosses can use and (b) set the minimum wage for undocumented workers to 3x the minimum wage for citizens and make sure they can file a labor complaint nice and easy. Would-be exploitative employers would quite literally lose the farm.
The fact that the US does the opposite tells us that underpaying and exploiting migrants is the entire point.