The reason we have this loophole is because many industries, particularly in the South, rely directly on immigrant labor. The republicans cannot risk alienating their consistency or further hurting the already brittle economy of Red states. That's why we get a constant flow of completely ineffective and performative solutions, like ICE.
Just start locking up executives who have employees that are undocumented, and the problem would disappear before your very eyes. But, building a wall is easier, and you can see a wall.