In any organized PvP, ie with people you know/trust/are communicating with, it is incredibly easy to permanently lock down a healer. If you are not doing this (or are not having this done to you if you are the healer)... it's not because they (or you) are overpowered but rather because the "other side" is terrible. If left to free cast, yes we are Gods. Simple solution, don't be bad and let us free cast.
This... so this. Even as a poorly (pvp) geared healer, if you let me free cast anything on this toon, haling or DPSing, I'm going to look like a god. On the other hand... even in random BG's on my 90 Rdruid, arguably one the more mobile healers, I can get caught up in CC chains that take me out of the fight long enough for my peels to die and me to follow right along. I mean I get CC'ed for a solid minute or better if they aren't actually hitting me through it.