In Classic, Alliance was just this innocent people that built buildings and had leaders who helped killing raid bosses.
Meanwhile Horde was this aggressive beasts who had the power to Destroy alliance but they were too busy
In Burning crusade, Horde played a bigger role than the alliance.
Speak of felorcs (Old horde) Etc.
And at the end of the expansion. Alliance played a bigger role (Velen in KJ fight etc).
Wrath of the lich king: Alliance played MOST of the expansion. Hell Bolvar fordring [the once old npc that was located in stormwind who was alliance is NOW the NEW lich king]
Tirion fordring was alliance at least and now is in argent crusade.
Thassarian played a bigger role then kor.
The lich kiing (Arthas) was once an Alliance.
And now.. This new expansion; cataclysm just changes everything in both worlds.
the hordes are having troubles with their very own leaders, meanwhile alliance work as a team.
the horde have destroyed and reclaimed almost all zones in cataclysm meanwhile alliance have bases somewhere around them.
The Hordes mostly have quests like, kill this alliance player, and stop this alliance person from getting this specific item, burn this alliance building and (YOU WILL 100% notice that once you level from 1-to 60) and you'll remember me for posting this)
meanwhile Alliance have quests such as: Use this vehicle to stop these fire elemenents and use this book to teleport to this place and put that item on it so it can explode) and Have a meeting with this specific horde npc and give him that item since he works as a spy. (You will also notice this) but it has less Alliance vs horde quests.
Now your questions are answered.
Varian and Garrosh will also play a big role, just because varian isn't showing up in some quests doesn't mean he wont, i'm pretty sure u haven't done the quest chain from uldum where Varian tries to help that weird tiger race? dunno whats the name from killing themselves.
Since most players that record videos are horde, thats the reason your not seeing alliance quests that is involving Varian.
As for Garrosh. He will also be seen alot during quests.
blizzard has already stated they showed Lich king too much and he started to look like a cartoon episode. do this quest, ull see him, do that quest, you'll know him, do this other quest, you'll find him.
and they already said that deathwing won't show alot, instead the faction leaders and deathwings eles etc will do his job for him.