My posts here have been simplistic and incomplete on purpose - but I genuinely thank you for sharing citations, your thoughts, and so forth. Education never stops. Just know that the words in my posts don't aim to be a sort of comprehensive analysis.
I understand that your posts do not aim to be comprehensive. Mine also are not comprehensive on the topic either, that is why we must ‘focus’ our arguments on the ‘one key’ factor that determines NBC and that is ...
... at the time of the child’s birth, was the child a citizen of a foreign nation and if so, then that child is not a ‘natural born’ citizen, let alone a citizen at birth. Until the US citizen parent acts on that child’s behalf in conferring, through statute law, their citizenship upon the child, that the child is an alien. Had the Cruz’s chosen to remain in Canada, the only way for Ted to become a US citizen would have ben for him to go to the US Embassy in Canada, renounce his Canadian citizenship and then meet all the requirements of residency, etc that is required of one born abroad of one citizen parent.
Where only one parent is a citizen, the child at birth may or may not be a citizen, it depends upon where he is born and the citizenship laws of the foreign nation of the foreign parent. And even this all hinges upon whether or not the parents are married and international law, from time immemorial, has concluded that where parents are married, the children follow the nationality of the father.