I'm not sure this is related to history because it's more about grammar and prominence.

World War I and World War II are distinct events that have shaped world, especially European + imperial/U.S., history. They're special, in a way. No one would say "Opium War I" because it sounds strange. Without already knowing about it, it sounds like a war related to Opium in some way. But WWI and WWII? That's a completely different case, even if someone's light on the details. They're two culturally important and related events that redefine Europe's borders, ideologies, alliances, and changed the international balance of power. They're THE world wars. There's no introduction necessary, so a specific article "the", and therefore first/second/third, is not required to talk about them. Even though the Opium wars are important, they're not events that defined the last century like WWI and WWII did, particularly in English speaking countries. If I said OW1 and OW2, people are going to guess it's a reference to popular media like Overwatch unlike WWI and WWII whose meanings are clear. I don't need to use "the" to specify the world wars numerically.

If "the" is used, however, then "first/second" is must be used instead.