Sure, but it will be a bit harder to make modifications once we "steal" it back when all the company publishes are the binaries. The GPL ensures that the source code is available for modification, and without copyright this would not be the case.

The 14th amendment says "All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.", so presumably your quick, boring solution would require another amendment, which doesn't seem particularly quick or boring. Unless children of illegal immigrants are not "subject to the jurisdiction" of the United States, which seems unlikely since many such children have been granted citizenship.

I (as will shortly become obvious) am no economist, but presuming that some US companies do business with people outside of the USA, if we are taxing those businesses are we not also gaining some tax revenue from people who are not in the USA - i.e. who are not us?

I'm also curious why, if business taxes are so bad and only appeal to the ignorant, just about every country seems to tax businesses. Do we lack non-ignorant people setting tax policy throughout the entire world (give some of the other laws created, I wouldn't doubt it for a minute) or are those setting the policies simply pandering to the ignorant masses that elect them?