“...and subject to the jurisdiction thereof,...”
I am not a lawyer or judge but I am fairly certain that clause has a definite meaning and I don’t think it was added for no reason. To interpret it to mean that anyone born on American soil is a citizen, regardless of whether the mother may have entered the country illegally an hour before the birth, is to say that it was added for no reason and has no meaning.
If you read the debates on the 14th, and the later statements of the congressmen and senators involved in passing it, they clarify what they meant. Oddly enough, the verbiage was much clearer as to what they meant before they changed it to it's final form.
The civil rights act of 1866 was the precursor to the 14th, and it is quite clear as to their intentions.