That shows a lack of imagination. There are plenty of solutions.
And yours would be?
Absolutely, but they're most effective if used in conjunction. Cutting off the welfare freebies for one. Heavily fining illegal-hiring employers for another. Considerably beefing up the border patrol for yet another. And of course eliminating the anchor baby provision in the 1965 Immigration Act. ...heck, rescind that entire piece of garbage altogether. Finally, cut off federal aid to all sanctuary cities.
....and then watch the hordes who have no intention of assimilating into American life deport themselves. Won't take too long at all, I suspect.
As far as legal immigration is concerned (kommie Kinsley insists we talk about that as well), the selection process needs a complete overhaul. But we can start by eliminating all Muslim immigration. Yes, all. Not one more Mohammedan until that culture can civilize itself. ...which could very well be never. And third-world immigration as a whole should be de-emphasized, which of course would automatically happen if my suggestion in regarding the rescinding 1965 Immigration Act were ever acted upon.
Essential reading: The 1965 Immigration Act: Anatomy of a Disaster