Actually shadow wouldn't be that hard to give a few buffs here and there and people would be happy. the reason that people complain is shadow has been behind in pve damage all expansion and has also received constant nerfs, most of them relating to there strength in one particular comp and because they did not want to address the real problem of symbiosis shadow lost things instead.
A noteable example being shadows offhealing which was grounded, shadow already struggles out of all the casters as the ONLY cast that has to manage their mana. Now all other hybrids are far better at clutch offhealing i.e. putting out a noticable heal when it matters.
To reply more directly to your point, I don't expect all 3 specs to be balanced for the most part holy isn't usually that strong though its been doing well this expansion. I do expect shadow and 1 healing spec to be pvp viable. Much like with druids I expect 1 healing and 1 dps spec to viable.
Warrior have actually had the option of prot in arena in wrath and prot has actually been the go to flag carrying spec upuntil blizzard decided they didn't like tanks in arena.
Shadow priests make continuous threads because "train shadow" is the tactic for majority of comps with a melee involved. Its a frustrating game to play.
I'm not sure why you don't want to see shadow priests in arena? I'd like all specs to be viable but no spec should be a binary Look its X train X and we can have a easy game/chance at an easy win.