It strikes me as strange to insist in this case on an explicit definition in the Constitution itself, given the fact that the Constitution routinely uses a lot of other terms without defining them; and so, quite a few interpretations in many other cases (not just regarding natural-born citizenship) have been based on discerning the intent of the framers and determining their likely use of language as understood at the time. Why is that not allowed now?
Because at the time you had at least two different schools of thought on the definition of natural-born citizen. The true test is how it is defined in federal law or in Supreme Court decisions. In three of the four cases mentioned, the circumstances of birth were not matters before the court at the time. In the fourth case, the Ark decision, the court ruled that Ark was a citizen of the U.S. from birth regardless of the nationality of the parents. Again, since the Constitution only identifies two forms of citizenship, citizen at birth and citizen by birth and natural-born citizen are all synonymous.