“I hereby declare, on oath, that I absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty of whom or which I have heretofore been a subject or citizen.” That’s the end of the story, right?
Not really. U.S. law does not apply in the other 190-odd countries and territories on the planet; other legal systems have no obligation to take notice of an oath to U.S. authorities unless their own laws tell them to. And the U.S. government, in practice, does not care if resident U.S. citizens hold other citizenships. (It cares very much whether non-resident citizens hold other citizenships, and demonises it as a method of evading taxes, but that’s another story entirely.) However, some countries of origin do care: their nationality laws prohibit dual citizenship, and require emigrants to report when they have acquired another citizenship so that the loss of their original citizenship can be formalised and recorded. Up until the 1980s, the U.S. also prohibited emigrants who naturalised elsewhere from retaining U.S. citizenship.
What’s the rate of compliance with these single-citizenship laws? Not very high; perhaps half at most, judging from Japanese and South Korean data. In a minority of cases, failure to report your new citizenship to the government of your country of origin may indeed represent an attempt to game the system. However, in most cases, it’s simply due to benign neglect: you are no longer under the jurisdiction of the “old country”, and have no future intention of exercising any rights there, so you don’t bother with the rules of their system. And of course, civilised countries do not presume guilt in such cases, nor impose life-altering fines on emigrants for failure to comply with obscure paperwork.