Read the end of Last Flight. There you have a fight against undead with combat heals. And to heal somebody can't be more complex, than e.g. to call a meteor shower like Solas.
Yes. One example in a very special situation is the correct one, and the game that follows literally everything else we've heard about the subject is the lorebreaker.
Sarcasm aside, yes it is more complex. Largely because the mage isn't actually doing the healing. They're summoning and binding spirits of compassion, and they do the actual job. But imagine what would happen if you gave Cole a bunch of organs and limbs and told him to stitch them back into the places they go. Even assuming he did it and got all the way through, I can't imagine him knowing things like where a gallbladder is supposed to go, and he has an actual human body to compare to. Spirits who've never been in the world before would have an even worse idea of what a person is supposed to look like, so the mage needs to pay constant attention to what they're doing in case they try to grow skin on the inside of the patient's lungs, and that's not even including what to do if a spirit gets distracted and wanders off. I don't have firsthand experience with either, but I'd say that takes longer and is more mentally taxing than a simple meteor shower.
But even if it is easier, it just so happens that none of the companions are good with it: Vivienne is trained in close-quarter combat and defensive magic. Solas specializes in manipulating the veil, and he hates binding spirits to his will. Dorian is from Tevinter (blood magic is sort of the opposite of healing) and a necromancer (which does involve binding spirits, but only the ones that show up when people die. That's not the right type). The Inquisitor has to take whatever teachers the advisors can scrounge up, and regardless is supposed to be fighting and leaving the healing to people who've actually studied anatomy beyond basic first aid.