While you are required to use your US passport to enter the country, whether you are required to upon leaving is not so simple. As there is no exit screening, the only way that your exit gets recorded is by the airline. Airlines generally record the passport you are using to enter the destination country, not the passport you are using to leave the US, so while the law may state one thing, in practice, the reality is by necessity, different.

Have you done a survey of this? There are many countries where this is not the case.