It's not technically an Alliance story either. Stromgarde has held no place in the current Alliance and is currently occupied by the descendants of people the old Alliance cast out of Alterac. There's also a Trollbane in the Horde and one in the Alliance. It could be a great battleground showing the war in the Eastern Kingdoms while we're battling in Orgrimmar, or it could be a good opportunity for co-operation after the fall of Hellscream, but it's neither "Alliance" nor "Horde" story at the moment.
The city state of Lordaeron (not to be confused with the region of the same name) was settled by former citizens of Stromgarde, and the High Elves -- now Blood Elves -- of Quel'thalas only joined the Alliance because of their debt to the Stromgarde (Arathi) bloodlines. And Thoras is dead. When the King dies, the Prince inherits. I know it's hip these days to sell wow accounts assume the undead aren't people -- but Galen's still sentient. He is still in line for the throne. As for Danath... he's been gone a long time. The last thing the Alliance needs is yet another do-good Warrior King to come in and save the day. Oh I know! Maybe Danath can be the embodiment of buying wow accounts the Wild Cat, because he's so fierce, and then he and Varian can go join the Super Friends together!
By your standards Stormwind is Lordaeron lore as well since it was settled by the last of the Arathi nobility (the Lothars) and was a member of the Alliance of Lordaeron. So, you know, that doesn't work. Further, princes don't inherit unless the king names them to do so. Every legitimate spawn of a monarch is given the title of prince or princess, but they don't all become king and queens. Sometimes the throne passes to the king's brother or his nephew (of which Danath is, btw). When Thoras died Galen did not become king even when he was alive. He either wasn't named as heir to Thoras at all, or was prevented from exercising that claim -- both of which call into question the legitimacy of his claim. He either doesn't have one or was so weak he couldn't.