Well, this is a bad (and incredibly expensive) idea, I agree, but....the ruins of the wall will be a cool world heritage site thousands of years from now.
There are lots of very extensive, interesting fortifications throughout history, some of which are quite long. The
Inner German border for example.
I've got to say though, how exactly would you guys reduce illegal immigration? It might be in decline, but it's still significant. Do you think there should be no restrictions? Do you consider more enforcement a bad thing? What about Mexico, which may not benefit from free movement?