You can move while casting if you hotkey. You can't if you click. Yes, one really is better than the other, otherwise clicking wouldn't be such a huge disadvantage in PvP -- and it is. I was a clicker in another game years ago. I got better when I stopped being a clicker, so I speak from personal experience.
I never played WoW.
I don't even have the AoE heal yet (level 43) and I don't struggle to keep DPSers up, even if they pull before tank. Is it annoying sometimes? Yes. Should they be doing it? No. But if you *ahem* hotkey you also switch targets more quickly/efficiently, so again -- a healer should not be struggling to keep both DPS and tanks up, presuming DPS aren't "standing in the fire" etc. or pulling six silvers at once.