The reason we healers DPS

[Freyt]

We don't just stand around idly. We carefully observe party hp levels always prepared to heal once we see anyone's hp drops by a milimeter xD

First, you don't need to heal a millimeter of HP. Not even Eos does that.
Second, you can do what I do and watch HP levels while you DPS. You have 1 major attack option to spam, you don't have a whole combo to muddle your brain over.
Third, if for the rest of the fight no large damage is going to come your party's way, then yes, you are standing around idly, even if you're looking at the HP.
Fourth, you don't need to dedicate a cast time to most of your healing. You know when an attack is going to happen, and so you prepare mentally for using an ogcd in between casting Stone, Malefic, or Broil.