Sorry, again, this definition for jurisdiction as it pertains to the 14th Amendment is the standard interpretation under current precedent being taught in law schools today. And there's a reason for that. Yes, there are other interpretations, no they are not generally held to be legally valid by US courts.

Namely, because it would otherwise cause ridiculous cases where a pregnant (but legally here on a temporary stay) tourist commits a crime here, a case is brought against them, and they give birth while awaiting trial. That child is not suddenly a citizen because their mother was held within the US legal system (i.e. under US jurisdiction) at the time of their birth; under current precedent, they would be recognized as having their mother's citizenship, and not US. An interpretation of the 14th Amendment to mean "can bring a criminal case against" would mean we see this, and we don't.

The jurisdiction carveout of the 14th Amendment was designed for very specific groups of people, only some of whom (diplomats) still need it applied (Native Americans are now just citizens with normal birthright, and there are no occupied territories), but written overly broadly at a time before immigration was a standardized process. Ergo, it's difficult to tell if the authors of the 14th (and such things matter in English Common Law and its derivatives) intended it to be used in the way it's been applied to people other than those groups.

Current precedent is that the children of legal immigrants and legal non-immigrant alien residents have birthright citizenship under the 14th Amendment, and that their parents are "subject to the jurisdiction thereof". The jury (or rather, the judge) is still out on whether the same applies to those here illegally. We'll have a hard ruling on that question in a couple of months, until then, it's largely speculation leaning on the side of "yes".