Do you really want to write into the law that illegals aren't subject to the jurisdiction of the United States? Open the jail doors ...
The point is that by being here they've evaded the jurisdiction of the US, not behaved as if they're subject to it. Thus, a citizenship on those grounds is not supportable.
They are within the jurisdiction, but are not American subjects. Get clear on the terms before constructing a virtual strawman.
Are you aware that prior to the Indian Citizenship Act of 1924 American Indians who remained loyal to their tribe did not receive automatic citizenship, no matter where they were born inside the country? That's because they were not subject to the jurisdiction of the US but to their sovereign tribe. It took an act of Congress to change the law.
That did not mean however if an individual had committed a crime inside the US they would not have to face the criminal justice system or would never be subject to its penalties. Your "Open the jail doors ..." is a strawman argument.