The general consensus of the Vanilla crowd is they preferred it when Pallies were Alliance exclusive and Shaman was Horde exclusive. Toward the end of Vanilla's lifecycle some folks on both sides complained the Paladin/Shaman was too OP for the Alliance/Horde to stay faction exclusive and thus, the other side was given the Paladin/Shaman class in TBC. DKs and Monks were given to both factions in WotLk and MoP and of course, new Race/Class combinations were introduced in Cataclysm.
Pressing the reset button on Paladins and Shamen (and by that I mean making the Alliance/Horde exclusive again) probably wouldn't be a good idea at this point so I'll kick the question to future classes.
On second thought: What if the class names and class abilities of existing classes were changed based on their faction and race? After all we already have Heroism (Alliance) and Bloodlust (Horde).
A few examples that come to mind:
Night Elf Mage = Highborne
Blood Elf/Undead Hunter = Ranger/Dark Ranger
Orc Warrior = Blademaster
Human Paladin = Crusader
In doing that, classes become diverse based on race and not faction. I'll leave balancing it to someone else but the lore's always been there and from a programming perspective it's doable with the existing technology.
Getting back to the original question I want to pose, though: Would you be ok with new classes being faction exclusive? Both factions would get a new class each but the other would never get it. For example The Alliance would get Shieldbearer (Melee DPS/Tank Hybrid) and the Horde would get Axebearer (Pure Melee DPS). Again, that last sentence is just for example purposes.