I'm not 100% percent sure about "regardless of whether it is part of a city" part". place=suburb exists for a reason, which here means "an administrative element that is part of the city". If a city has many districts and counties in it, then all should be tagged with place=suburb, because it's a more precise tag to be used. In Vietnam, we also have ambiguous cases like that, such as "quận" for districts and "huyện" for rural districts/counties, and currently we are (trying) to follow this convention.