I would include the USA, with the caveat that in the US being sent to the military is often seen as a punishment for rich children where as in the Middle East being sent to the military can be an opportunity to build an independent power base for yourself or your family.
The USA has a volunteer military. Occasionally there are cases where the criminal court system might agree to dismiss a minor charge if the defendant enlists. But that doesn't happen to rich people, or those joining as commissioned officers (pilot track).
