Are the companies employing them paying the same taxes on these “workers” they would be paying if you or I did the job? I think not. The really ugly truth they and their visa loving corporate welfare folks are tax dodgers through and through.
If it becomes as expensive to hire them, as it does to hire American citizens, problem solved.
Make the penalties for hiring illegals high enough, and do enough actual enforcement of the law, and companies will stop hiring illegals.