There is no such thing as an impenetrable wall. You can scale it with the right ladders or dig under it. Best thing to do is to go after and fine the living hell out of the American employers with threats of property confiscation and jail time. You will never stop this until the employers face severe consequences. Also no voting or welfare period. Treat them as lepers.
I was assured by some here that we MUST have a wall because future Democrats would not police the border.
But guess what, democrats in power could cut patrols while the Mexicans cut “the wall”.
So your idea is probably the best.