Birthright citizenship existed long before the 14th Amendmnet, but back then it was only restricted to white people.
The 14th Amendment was passed in 1868, before we had immigration laws and our borders were open. The first laws restricted criminals, Chinese, and Eastern Europeans.
People from the Americas (Mexicans, Canadians, Central Americans, etc.) were considered "white" and a visa for entry was not required for entry into the US until 1965.
So can it be said that birthright citizenship was never intended for undocumented entrants? I suppose, but since this whole documentation requirement is relatively new this argument sounds spurious.