Well, I won't go as far as to say it's 'not common' around the world, it's just normally found at higher ranks than the US. In the British Army, for example, you find them on "Field Marshal" rank, which nobody holds right now. That said, much as the oak leaf cluster is affixed to medals in the US military to indicate subsequent awards of the same medal, the lowest form of commendation in the British military is to be Mentioned in Dispatches and is signified by the wearing of an oak leaf on the campaign medal in question.

Best as I can determine, the first official use of the oak leaf in the US is found in the US Navy, when the adornment of the coat of 1830 is described. The Navy started to use insignia to display a staff officer's branch. All line officers wear a star, all staff officers wear the branch insignia which, even today, is some variant of an oak leaf. (Chaplains being the one exception).

The use of the oak leaf for rank dates to 1836, when it was created for LTCs and Majors of the Army. The Navy didn't get on board with that insignia until the Civil War, Prior to then, they were all grades of Captain.

The oak leaves are also found as the 'scrambled eggs' on service caps for field grade officers and higher.

As for why oak leaves in the first place, you have to go back to Rome. Cindee Herrick of the Coast Guard Museum explains that oak leaves are a symbol of authority dating back to Roman times and earlier. Roman emperors and senators were crowned with wreaths of oak leaves. The oak is an ancient fertility symbol of the male principal. For the Romans, it was a symbol of service to the state. In some cultures, the oak tree is holy. It has taken on civic authority in some cultures where marriages and trials were performed under an oak tree. https://www.madetomeasuremag.com/the-oak-leaf-and-the-acorn-a-look-at-coast-guard-dress-caps