One of the most idotic aspects of this automatic citizenship for children born to illegal aliens is that the same right is not afforded to children born of alien parents here on a visitor's visa. When that happens, the parents are told to register the birth at their nearest national consulate or include the child on the passport, as the case may be, to transmit citizenship to the child under their country's nationality laws.
Someday, a foreign national denied U.S. Citizenship under such a birth should have the right to sue for unequal protection given to them versus a child born of illegal aliens. It doesn't make sense.
I have not heard this being done. It's common for Mexicans to be arrive in the U.S. on a visa , 9 month pregnant and claim citizenship for the newborn child.