I used to have the same opinion, but after reading some dual citizenship cases, suggest that a bith on foreign soil may have some consequence.
The consequence of birth on foreign soil is that the foreign country may claim the person born there is subject to that country's laws, "under the allegiance" as it were. This could become a substantive issue, if the president was back to the country he was born in (as a practical matter, probably not, as he travels as the head of state, a super-diplomat, if you will), but in principle, the other country may (and is entitled to) make a claim, just by the accident of birth.
The founders held that allegiance flowed from parentage, not from place of birth.
By common sense, it has to be recognized that the child is utterly unaware of its place of birth. For a very significant part of his life, his family is all he knows. That is the only thing that is likely to influence allegiance.
What a foreign country may claim or wish is so utterly irrelevant, unless the child is raised there, which is why the return to the home of the parents is important.