You seriously don't think there is a difference between a documented LEGAL immigrant and an illegal immigrant? How does one prove their parents were here legally? No one is talking about making this retroactive.
This isn't about curbing LEGAL immigration, it's about the rights of LEGAL citizens, alien or native, IMHO.
Not every illegal immigrant snuck across the border. IIRC, most illegals entered the U.S. legally with visas and have overstayed. So yes, sometimes it is a matter of paperwork. And questions of how to prove it are valid, IMO. Are we going to DHS agents stationed at hospital to check each parent's citizenship or resident status? Or would you need to carry around you parent's birth citizenship papers along with your own to prove citizenship?