Would you feel the same way about the Second Amendment? (Rhetorical Question).
Just like the Founders couldn't have anticipated Chinese Birth Tourism (which isn't nearly as dangerous as you think), they also couldn't have anticipated inexpensive semi-automatic weapons.
We can't pick and choose which parts of the Constitution we want to follow.
I'm just not seeing birth tourism as a "suicide pact". There are 300,000 resident alien births every year. While this might seem like a lot, it only represents 0.1% of the population. Many of them will probably never exercise their privilege of American citizens.
In some ways, it could be a benefit. More Chinese-Americans? I'm probably biased, but I just don't see that as a bad thing. I never met a Chinese person who wasn't willing to work their ass off to better themselves. More of that, please!!!