Interesting question, I never realized that.
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One issue I have with this idea is that there is no indication that the SC and the high elves at the lodge have any association or common interests with each other. And we know from official blizzard statements that there isn't a clear example of what a high elf is, meaning that the small pockets of high elves around (ie SC, highvale, Allerian stronghold) all have different ideals, interests, goals and ideologies. They likely wouldn't see eye to eye on many things and likely view things differently. We have no indication that they would even want to unite at all. They've been separated for a reason, and have chosen to live as separate groups likely because they have no real intent to unite.
It'd be like requesting all the orc clans on azeroth to unite, despite many of them having little to no association or common interests with each other (such as if the frost wolf and dragonmaw orcs united).
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Why were the SC absent in this war as a collective militia group? Why are there only 2 high elf individuals participating?
Anduin states in CGI cinematic that the Alliance are nearly out of troops and they'll have to start using farmers soon. If the SC were an Alliance militia group, not a militia group of the Kirin Tor (ie neutral nation), then I'd be pretty pissed (if I were Anduin) if this Alliance militia group decided not to turn up to the war and instead had 2 de-facto representatives sitting on some air ship.
So either the SC are an Alliance group who practically abandoned the Alliance during one of their most bloody wars (wouldn't be the first time alliance high elf exiles abandoned those close to them), or they're a militia group of the Kirin Tor and as such their neutrality prevented them from participating under the banner of the SC and as a collective unit.