(Disclaimer: I'm not a raid healer, so this is all second hand info, I also play SCH, and not the other healers, so I recognise that they have more intensive MP management, which can restrict DPS)
In all honesty, raid healing is a different beast to dungeon healing as a whole. You tend to have a dedicated healer who spends 100% of the time (except the odd enrage push) healing, and you have the off-healer who's job is to DPS when they can and contribute to healing when they are needed (duel tank mechanics and heavy damage output). When in a dungeon scenario, I would label the healer in the offhealer camp, healing when needed and spending the rest of the time DPSing, which isn't to say that they are a DPS, rather saying that the button that is pressed on any given GCD should be the one that will benefit the party most.
This is all off topic anyway, so I will segway back by saying that healers do not need parsers, and the devs are trying to discourage the requirement of healer DPS with accuracy limitations, but what this means is that the job falls back on DPS to pick up the slack. No role should be complacent in their job, it just so happens that a complacent DPS doesn't directly cause wipes, and that is why they seem to get a free pass, which isn't how it should be in my eyes.
Edit: regarding your comment about "relaxing in a stressful situation". The answer to that is that you hit the best button for the situation, if you have to heal then heal, if you have room to DPS then do so. All of your buttons are there for a reason and should be recognised as such. Now obviously you don't have to use them all (fluid aura being extreamly situational for example), but at least recognising where you would use each skill is recommended (if not essential) for hardcore content.