I would actually say the recent schism is more what sets them apart now - rather than making an argument of shared historicity, I would argue the more recent separation. The High Elves of the Silver Covenant and Alllerian Stronghold (which I will just call "exiled High Elves" for simplicity moving forward) have altered their heraldry; adopting blue/silver as opposed to the original red/gold solar motifs that they once had, or the red/black motifs the Blood Elves now favor. Socially as well they have moved somewhat away from their Arcane focus, given that the core of the modern exiled High Elves are likely not Magisters but rather formed more predominantly from Farstriders and members of the Priesthood of the Light (both of which seemed to be the stronger opponents of Rommath's practices such as Mana Tapping).
The dire straits of their society, such as their reliance on Dalaran's charity as well as the paucity of their settlements is even more of a defining trait - they don't have a homeland unlike their Sin'dorei peers. The High Elves on the other side of schism are effectively refugees and exiles, unwelcome in Quel'Thalas and alternatively too proud or too vengeful to forgive the Sin'dorei for the original schism and return to the fold, so to speak. Given Auric's appearance and character in WotLK during the Quel'delar questline I would say it is unlikely his people has reintegrated with the Sin'dorei, and the words of some NPC's within the Allerian Stronghold speak to a pretty open opposition to the practices of the Sin'dorei (e.g. holding the same grudge that Silver Covenant members do).
I don't disagree that racially speaking, or in terms of heritage, that Blood Elves are High Elves - I simply maintain that the schism between the two factions of High Elves, in the form of the expulsion of those who refused to adopt Rommath's practices to protect them from Arcane addiction, has resulted in two distinct and discrete factions which could constitute the core of two playable races. The exiled High Elves having a deeper closeness to Humanity and/or adopting cultural elements from Humanity is actually another defining trait that sets them apart from their more traditional brethren as well.
In my view "Blood Elves are High Elves" is a true statement that doesn't really define a strong lore-centric reason for these two factions not to be realized as distinct and discrete. Prior to the Void Elves include as a playable race I would've argued that silhouette and population would've been your main reasons not to include the exiled High Elves as a playable race - but the Void Elves' inclusion diminished both of those rationales: they are both few in number and silhouette-wise they are the exact same as the playable Blood Elves. Zandalarai Trolls are Trolls, Highmountain Tauren are Tauren, Void Elves are High Elves, and Nightborne are Night Elves - all those statements are equally true and yet those Allied Races remain a playable subset of their larger, overarching groups.
The faction argument, or what I like to think of as the balance argument, is pretty much the only argument remaining to prohibit their inclusion. The Horde has Nightborne (a Night Elf analog) as well as the Blood Elves, whereas the Alliance has the actual Night Elves and now the Void Elves (a High Elf analog), keeping a balance between the extractions of Elves. Adding the exiled High Elves to the Alliance, or to the Horde, throws this off somewhat and makes it unlikely unless *another* derivative of Elven extraction is created (which seems unlikely).
I don't disagree with the argument of equity, in that sense, I just disagree with the lore-related assertion that the two factions of High Elves aren't distinct enough.