This is probably more of an Alliance problem than it is a Horde problem, but what race would you add to both factions that add a real, new, novel choice to that faction.
As an example, the Vanilla human joke that’s always been with WoW is: On the Alliance, you can pick an Elf, a Human, a short human, or a tiny human. There’s not a lot of difference between those three races.
Given all the races on a faction, which race would add the most unique RP options?
If you want something really unique, you could have the Ankoan. Androgynous fish people!
I’d really love to see one of the factions get a plant-based race. That’s something we don’t have anything like. Maybe in the Emerald Dream expansion.
Saberon
You think we have a furry problem now?? Add kitty people! Especially if the females are non hunched over versions of them that look like housecats rather than the hunched tigers the males are.
For Alliance, I’d say the Arakkoa or Jinyu would be a good choice.
For the Horde, Saurok or Saberon would be my pick.
Yeah, they’ll likely get that. I just worry that we’ve done Animal-people a lot.
At the end of the day Alliance players will just ask for more elves.
Give me a tail and that’s all the diversity I need.
That solution can be achieved when they get rid of the factions.
Animated tables for the alliance
Animated spikes for the horde
Easy
Alliance:
-Arakkoa
-Sethrak
Horde:
-Broken
-Ogre
This expansion opens up the option of Stoneborne. It’s a missed opportunity of Blizzard doesn’t take it. They are a faction that can easily be made neutral and at the end of it choose which side they wish to represent.
Lizards…
Alliance could have Sethrak. A proper monstrous race! 
Horde could get Kelfin or Ogres. Something like that.
Or Arrakoa for Alliance and Sethrak for the Horde.
(I really just want Sethrak playable, preferably on Alliance. Partially for reasons OP listed)
Since everyone is interested in a third faction how about a hillbullie kobold ,grumpy, aggressive little cave dweller. They are already in the game so that part is taken care of and can be used on both factions. let’s steal their candles!
Crab people.
Something that uses a unique skeleton and is not bipedal.
Something not elf or animal based.
No matter what, everybody knows the Alliance will be mostly humans and the Horde will be mostly elves.
Mogu would be the best race for the alliance imo.
They would bring a good Conqueror mindset to the alliance and give more support for Genn and Tyrande to go on the warpath.