So you agree, and an alien isn't "subject to the jurisdiction, thereof", meaning the Constitution.<quoted text>
We do this all the time and by doing so we never bestow upon such individuals citizenship. For example, diplomats. If that were not the case, then it wouldn't make any sense to call a person an illegal alien because he/she would be automatically and immediately become a US citizen the moment they became "subject to the jurisdiction, thereof." And that does not happen.
Well how is it we can prosicute them in a court of law, if they break out laws.