You assertion would have merit, if we deleted the first 2 words of Section 1. “All persons” is pretty defitive. IMHO, the term “All persons” means everyone, legal, illegal, blind, dead, living, left-handed, blonde, fast, slow, short, tall, fat, skinny .... pretty much everyone.
So, does “All Persons” apply to a couple from, say, Canada on a weekend holiday into NYC... and she has a baby at a Manhattan hospital?
According to your assertion that all persons means EVERYBODY regardless of whether or not they are subject to its jurisdiction means that if a family is vacationing in the US and the mother gives birth, then the baby is a US citizen, or if a diplomat present in the US has a baby in the US it is a US citizen rather than a citizen of the country of which the diplomate is a citizen. The author of the citizenship clause argued that this is clearly not the case.