Let's use some logic here, if they aren't subject to the jurisdiction thereof", then they can't be in violation of US law, right? In this regard, their immigration status is immaterial.
You are subject to the jurisdiction thereof unless you enjoy diplomatic immunity. It isn't a relative condition. Like pregnancy, you either are, or you are not. You can't say that you're "subject to the jurisdiction thereof" if you murder someone, but at the same time say that you are not "subject to the jurisdiction thereof" for purposes of the 14th Amendment. It's as simple as that.
I'm not saying I wish it to be that way, but I understand that is the legal reality as the law exists today.
You are subject to the jurisdiction thereof unless you enjoy diplomatic immunity
Offering your own conclusive speculation as to what a particular English language phrase might mean to your mind is interesting, but it takes us further away from points relevant to the question of whether Congress could by statute enforce the Fourteenth Amendment in a way that interprets "subject to the jurisdiction thereof" to exclude childen of foreign nationals here illegally and to what extent the Supreme Court would accede to that view.