> Most of us are only citizens because someone up the chain was born under this rule.
This understates the situation. All of us who are not naturalized citizens are citizens only because of the birthright clause in the Constitution. The US does not have any other way for a person born here to become a citizen.
If the birthright clause of the Constitution stops being enforced, Congress (or more likely in our current iteration, the President) will have to create a brand-new set of rules determining which of us natural-born citizens get to retain our citizenship and which do not. There is no existing law to guide them, so they can make it up out of whole cloth.
More plainly: if we choose to eliminate birthright citizenship, whoever is running the country at that time gets to determine whether you are still a citizen.