It's somewhat of an accident that the Blood Elves are in the Horde. As High Elves they'd been part of the Alliance. Their 'conversion' to Blood Elves was recent. Their joining with the Horde was even more recent, and was not inevitable. There were doubts, and justifiably, that this more-than-devastated nation would be little more than a burden. Surely a Horde that had only recently broken away from demonic influence would be wary of a race that was dependent on demonic power.
In terms of personality, it fits as well. Elves are generally arrogant, and high elves perhaps even more so. Why would they not stand alone, away from the savages and corpses?
They have their own problems, trolls and the Scourge. Remember, BC was long before the Lich King was defeated. Could they really afford to go marching off to someone else's war with the many powerful Alliance armies on the continent? But perhaps that's irrelevant, since they have a powerful buffer zone against the Alliance: the Plaguelands and Lordaeron.
Who would become paladins? I still think tauren paladins sound ridiculous, even though I also think that Sunwalkers are a somewhat logical extension of druidism. There has always been a bit of a push for Forsaken paladins, but those also have various problems, even if they sound cool. Perhaps they'd be the inverse of the Blood Knights: rather than being so dark that even their brethren shun them, they'd be rejected for their embrace of the Light.
Geographically, Silvermoon isn't of much use to Horde players. Undercity already gives good access the north of the Eastern Kingdoms.
Most importantly, it's too late for World of Warcraft. The story already happened, not that that has necessarily mattered; Cataclysm was more than happy to erase player actions, such as killing Onyxia. Players are Blood Elves and I suspect would not react kindly to a forced race change. A splintering, as we saw with Pandaren is possible, but also sets an annoying precedent, because what race could not be justifiably picked apart? Break off the Dark Irons again, divide the orc and troll races, might as well just have every character pick its faction. Someone probably likes that idea.
This is where I think the idea shines. Or, gets exceptionally ugly.
Despite regaining the Sunwell, I do not believe the Blood Elves are particularly powerful still. They were hit far too hard and were never a populous group. If no longer under the umbrella of the Horde, they'd end up with a potential enemy: Sylvanas.
I'd love to see this dark... darker.... black hole swallowed by another black hole, but without the huge energy releases from gravitational waves... darkerest turn by Sylvanas. Why should her former brethren not rejoin her? Perhaps the Forsaken could find some use for the Sunwell.
This leads to her army marching right back up along the Dead Scar and her journey to becoming the Lich King-lite is complete. Might the Alliance, seeing the risks of the Forsaken gaining such a powerful source of magic, intervene? Things could turn out ugly for Vereesa.
Alternatively, they just get overrun by trolls and breakaway undead.