PvP Power isn't even a particular problem. Damage relative to health is a problem. Doing 20-30k a swing on someone that has 400k health is not enough.
All the same a healer can heal someone full in 2 casts. Many cannot even be kicked. You're left in a position where a damage dealer can't deal enough damage to kill someone before the healer gets off 1 or 2 heals and negates everything they did. On top of that in BGs there's 1-3 healers, and they can heal each other, becoming effectively invincible.
The issue is so bad in arena that they literally had to put dampening into the game, except dampening doesn't even do what it should. Dampening SHOULD increase a healer's mana costs rather than reducing their heal effectiveness.
But lets be honest, dampening doesn't need to exist. If healers were actually balanced in PvP, or damage relative to health was dramatically scaled up, arenas would be a faster experience.
How do you fix PvP? Expand diminishing returns on CC, nerf healers, nerf healers healing healers, increase damage players deal to non-tanks.