Blizzard seem to be debating the idea of declaring one spec per class as the "PvP spec", and I do think that's what they should be doing - instead of 34 classes, you're only balancing 11 (or 12, if they add a new class with the next expansion.)
So what if they decided to tune it so that healing and tank specs aren't good at PvP?
Consider: Every spec of every class has at least some self-healing capability, and as far as I'm aware, every spec of every class has at least some disables or other utility spells (like roots, disarms, silences, etc) available to them. So why do we even need dedicated healers and tanks?
Currently, healers are designed so that they more or less can't be killed by a DPS spec (or tank spec) in a solo fight, and I'm sure plenty of people have seen healers running around in circles tanking multiple players for a considerable amount of time before finally dying (or being rescued.) This is because of the balance emphasis on 3v3 arenas - if healers could be soloed by DPS specs, why would you bring a healer at all? And the reverse is generally true - because of a healer's generally poor DPS and the self-healing abilities of DPS specs, healers typically can't kill a DPS either.
This also typically applies to tanks - they can't be killed, but they can't really kill, either. Their job is to sit their ass on a flag, or carry a flag around, and if a single DPS could easily bring them down, there'd be no reason to bring them... and if tanks could easily kill DPS or healers, there'd be no reason not to stack tanks.
In my opinion, this results in somewhat boring gameplay, for everyone involved. When I play a tank, the only thing I can really do (especially now that tanking is done by mashing Shield Barrier and not, say, rotating Shockwave with Concussion Blow and then LOSing while those stuns are on DR timers) is grab the flag and run around - I can't kill people, and changes made in MoP also largely robbed me of the ability to effectively protect teammates (this is now pretty much exclusively the healer's role.)
This also applies for a healer, and even for a DPS. As long as tanks are around, you'll never really exclusively delegate defensive roles to a DPS, and you'd certainly never ask a priest to start turreting Smite instead of Flash Heal.
So why not just get rid of tanks and healers, and design PvP to be done with just DPS specs? Since this is the kind of change that would only take place during a new expansion, I don't think PvP would turn into a button-mashing burst orgy, either - you'd have plenty of time to develop it and pace it properly.