You may want to think this through.
If immigrants aren't subject to our jurisdiction then they aren't subject to our laws - by definition.
Good point, but that’s how many act anyway. . .however, failing to observe our laws makes them subject to immediate deportation regardless of being a legal or illegal immigrant.
“Jurisdiction of the laws” does not mean that Illegals can’t be prosecuted for violations. It just means, in that case, that they were born under another jurisdiction though within this country. The Anchor Baby issue was actually discussed when the 14th amendment was under debate and the conclusion of that was that there were to be no Anchor Babies.
Jurisdiction takes many forms this is just one of them. The concept grew from Natural Law.