Okay, here's what I think, ultimately.
I think people here on tourist visas are subject to the jurisdiction of the United States. I really do not think that a credible argument can be made that they are not.
That being the case, under the 14th Amendment, the children of birth tourists are citizens.
I don't think birth tourism is an enormous problem, but it's not anything we want to encourage. I think we could find ways legislatively to penalize and discourage it. We could require tourists to disclose whether they expecting to have a baby during their stay in the US, for example. Impose fines, and such.
On the other hand, I think there is some argument to be made that illegal aliens are not "subject to the jurisdiction of the United States." That argument might well fail in court as well, but I think it's worth making.
If it passed Constitutional muster, fine. If it didn't, then we could pass a Constitutional amendment.
All of this, again, presumes the will to do something. I don't think that exists. Clearly, it doesn't.
And I doubt it ever will. If it does, then this discussion becomes more than just theory. Until that day, it's really just academic.
In a limited way, yes. However, they are NOT under the complete jurisdiction of the U.S., which is what both Trumbull and Howard, the originators of the 14th Amendment's citizenship clause, specifically stated in the Congressional Record was required.
Case in point: some children born to aliens in the U.S. are born SUBJECT TO a foreign country's nationality law. Prime example: Obama.
That is PRECISELY why U.S. Secretaries of State and the International Arbitrator determined that those born in the U.S. to alien parent(s) WERE NOT U.S. citizens. They were SUBJECT TO A FOREIGN POWER and OWED ALLEGIANCE TO A FOREIGN POWER at birth via their alien parent(s).