Self-sufficiency. A healer should be able to do enough damage to fight a MOB if he or she needs to, just as a tank or DPS or crowd control class should be able to.
If my healer is exploring a new area and gets attacked by a giant spider that characters of other roles would be able to fight, she should likewise be able to. I will never forget the Midgard Healer who, unlike the Albion or Hibernia equivilant classes, was so weak that a grayed out MOB many levels lower could kill her. Not pleasant. Sometimes even the most group-oriented character needs to get somewhere on her own.
Fun : Playing ESO I have fallen back in love with being a healer. They have done some things right and some things wrong. I love I can still DSP and doing DPS can give my teams buffs and heal me. Healing does not just heal my team but also buffs my team and also debuffs who we are fighting. Even overhealing can add things. No matter what I am doing as a healer, Im doing more then just looking at HP bars. I don’t like that I have no control on who I am healing. The game picks that for you by the priority it thinks is most needed.
Mommy.
I made a joke post in the "One word how do you feel about tanks" basically saying tanks are the daddy, healers are the mommy and DPS are the unruly kids. The only difference here is that these (healers) are the classes that I like to main above all else. I am comfortable enough with saying I guess that makes me the mother in the situation who basically has to make sure daddy isn't being mobed by a gang of thugs, and the kids aren't playing with matches.
*All jokes aside Healers, Tanks, and DPS/CC are 3 parts that make up the whole. All these roles have their own value and at higher levels, all 3 should rely on the strengths of the other two to make up for their weaknesses. In general, I am not a fan of the whole solo mentality. I see the argument being made that tanks and healers should have the ability to solo content which DPS have the ability to solo. I agree with this, however, I think that the majority of Pantheon should be designed without the ability to solo in mind.