That was the intention.
Decades later a series of bad court decisions resulted in the re-interpretation of the clause in ways rejected by the folks who'd written it.
There is no "law" in the sense of a statute that creates "birthright citizenship". In fact, the whole business rests on nothing more than reversible court decisions.
If that happens, there are millions of Americans who will find that they are no longer citizens and must return to their native country somewhere else.
Do you feel lucky? If you want citizenship you'd best go ask Congress to pass a law pinning it down for you.
You are exactly right....all it takes is a re-interpretation as it was never intended to foster the "anchor baby" debacle...