He didn't "sneak across", he obtained a fake visa and thus entered legally. 'Closing the border' would not have affected him. Overstaying a visa is another example of entering the US legally. Again, closing the border won't help.
Crossing the border illegally will most certainly not be quicker, and time is not an issue to terrorists anyway. Try again.
You are proposing to blow money on measures against non-existent threats. This will take money away from measures against actual threats. This may lead to underfunded measures allowing a terrorist to slip through. If another terrorist attack strikes the US, enjoy being morally responsible for the event.
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