Why did the Constitution limit the power it granted Congress over matters of citizenship to naturalization? Because Citizenship acquired solely by any law passed by Congress cannot logically be anything other than naturalized citizenship—by definition of naturalization. It's logically impossible for any act of Congress to make anyone a citizen by natural law. At most, such a law would be declaratory of natural law—because a citizen by natural law is a citizen no matter what laws Congress may or may not enact.
In fact, given the Founders' understanding of natural law versus man-made law, it would have been a logical contradiction to grant Congress the power to change or define natural law on any subject, not just regarding citizenship—because natural law, by late 18th-century definition, cannot be made by a legislature or head of state. That's why Congress was granted no such powers in any domain at all. Such a power could be used, among other things. to change the meaning of words, including those in the Constitution itself. The dangers of that should be obvious.
If Congress had the power to make anyone a natural citizen, it would also necessarily have the power to strip citizenship from anyone it chose. The fact it cannot logically have any such power—and is granted no such power by the Constitution—is one of the fundamental protections against tyranny. The power to revoke even natural law citizenship by law is the power to commit any act against anyone that the sovereign power of war permits.
So why didn't the Constitution define the term natural born citizen? For the same reason it could only grant Congress the power to define naturalized citizens. For the Constitution to actually define the term "natural born citizen" would necessarily mean that that status would be granted by man-made law, and not by natural law. That's why the Constitution provides no definition, and why it must be a court that decides who is and who is not a natural born citizen by applying natural law principles—which is exactly how English common law handled questions of natural citizenship.
But the ratification of the 14th Amendment introduced into the Constitution a rule of citizenship that declared anyone who (a) was born in the United States, and (b) was subject to U.S. jurisdiction at the time of his or her birth, to be a citizen. Since the 14th Amendment is a man-made law, and is not natural law, the 14th Amendment logically cannot make anyone be a natural citizen. Nor does it create the logical contradiction of attempting to do so, since it makes no mention of natural citizenship of any kind, and does not use the term "natural born citizen."
If Congress gets to decide who needs to be made a citizen (naturalized), then it is automatically defining who does not. I’m sure you see that.
Current law says that anyone born overseas to one US parent is recognized as a citizen at birth. That is similar to every law Congress has passed on the subject all the way back to the first naturalization act in 1790.
So, we can wish and want and hope and dream and write all we want about what we think “natural born” means, but it doesn’t change a thing in the actual laws passed by Congress....who is empowered by our Constitution with authority over this particular matter.