You asked ‘ Are children born to illegals on US soil NBC?’
In my frame of reference such children are not NBC because of the requirements for parents to be citizens at time of birth. I believe the Founders wisely considered family allegiance to the USA be as a critical requirement for NBC to the extent possible to be ascertained. When the question arises I not only think of Mexicans or other Latin Americans but also of the two sons of the current President of Egypt who were born in the USA. I believe that the Founders wanted to make sure that the requirement for POTUSA was as ironclad as possible to assure a POTUSA had no foreign ties that might compromise their duties to/for the USA. The wisdom of their thinking and writing is being held to test under Obama and his enablers including even government officials.
I've already suggested that it may have been an inculcated understanding due to the remoteness of America at the time and the assumption that people born here were born to natives of the land, given that travel from Europe took so long. Also, the Preamble to the Constitution refers to establishing the Constitution to secure liberty to "ourselves and our posterity," meaning the citizen people and their citizen children.
That said, from the argument that a born citizen is one who is born in the jurisdiction of the country (and not just on the soil), a legal alien would be under the jurisdiction of the country, but I think that an illegal alien is still under the jurisdiction of their homeland, so their child born on USA soil one day after illegally crossing the border should not be a citizen.
I concur with your thoughts on the wisdom of why roots & family are important for eligibility to run for president.
I just wish the writers of constitution and the amendments passed thereafter would have explicitly stated what a NBC is. But it is not. Therefore all we have in interpretations.
Obama’s father was never a US citizen That fact is well known and indisputable. Since the SCOTUS has not overruled on Obama’s eligibility, a legal precedent has been set. Legal precedents carry a lot of weight. Whether you like or not, anyone born on US soil (even with a computer synthesized Hawaii BC) will be eligible in future regardless of his/her parents citizenship status.
I am willing to bet, if Rubio runs, the SCOTUS will NOT rule him ineligible. He was born on US soil of legal immigrant parents. Rubio should thank Obama for setting that precedent.
As for Cruz, it gets more muddled. He was born in Canada and both his parents were not US citizens at the time of his birth. And none of his parents were on official duty in Canada.