I'm sorry, but unless you can find a way of declaring certain persons born in the United States are not subject to the jurisdiction thereof, the plain meaning of "All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside," means if you're born here, unless your parents were diplomats so that they and you have diplomatic immunity and are not subject to the jurisdiction of the United States, you're a citizen.
I suppose we could declare anyone who sneaks into the US to be a diplomat, so that they and their children have diplomatic immunity, aren't subject to US jurisdiction and get around it that way, but then all the illegal immigrants who commit crimes can only be deported, not tried and punished for their crimes. Of course, that would still leave birthright citizenship for people whose parents were here legally and were not diplomats (e.g. on student or H-1B visas).