The aldmeri dominion only has 2 elf species, the third is a beast race and the orsimer and dunmer arent even a part of it.
On topic, the idea of an elf faction will never work do to fundemental issues the elves all have with each other. Void High Elves tend to hate blood elves, and the Blood Elves and Nightborne have low opinion of the night elve which is mutaul to my understanding.
This isn’t even getting to all the undead elves like banshee’s, dark rangers, and sanlayn.
The Elves don’t like each other, and are highly unlikely to abonden their current alliances for each other.