Good idea - but CLEARLY unconstitutional - you'd have to make an amendment editing the definition of a citizen - and it'd never pass - b/c then the gov't could easily just control citizenship to whatever pleases them for their good.
Not really, as the relevant clause in the 14th Amendment is "born ... in the United States, and subject to the jurisdiction thereof," An illegal immigrant or a tourist does not fall within the latter half of the requirement. On the other hand, the child of a legal immigrant does, even if they never attain citizenship themselves.
How so? Illegal immigrants are bound by the laws of the United States as much as any other non-citizens in the country. Also, given the use of "born", the text appears to refer to the child, not the parents, so being "subject to the jurisdiction thereof" is inherent for a person born in the United States.