I think one of the reasons the Cole split is so interesting, and divisive, is because on the surface it asks you to pick a path for one person, but really it’s a “who do you save” question.
Person A: Compassion, the lost spirit.
Compassion, a ‘physical’ manifestation of the virtue, came through the veil to help the mage-boy Cole, and found himself in a confusing and cruel world. Not understanding the world around him, he took on the identity of a Cole and lost the understanding of Being a Spirit. (The implication being that his other option was to become a demon). By helping him learn about the world, and unravel himself from this manifested personality- you save The Spirit Of Compassion. Returning him to the person he was before ehe got lost, Protecting him from future corruption/binding, and allowing him to return back to his home in the fade if he wishes. He is once again The Spirit of Compassion, manifestation of the Virtue, which was always his true form under all of the layers of obfuscation required not to become twisted by the material world.
But when he turns to you and says “you can still call me that if you wish” it really does feel like you’ve lost something. And you have!
Person B: Cole, the boy who was a spirit.
When a spirit of compassion came through the Veil, it helped a mage-boy named Cole. Something got a little muddled, and he lost the sense of who was Cole and who was Spirit. But he made a friend or two, learned that murder is only ok if the person is evil, and came to understand that there -was- a difference between him and the original Cole.
Now you have a New Person! Who is not the Mage-Cole, but shares his trauma. He is learning and growing, and becoming ‘more real’ . He has experiences unique to him and relationships unique to him. This, is the companion you bring into the inquisition. Somewhere between boy and spirit. You help/watch him grow: he expresses preferences, makes friends (and enemies) and learns a lot from the people around him. By the time he’s standing with a crossbow in his hands this is Your Friend Cole, facing someone who caused the Trauma that put him on this path. Forcing him to acknowledge that he Is something other than a Spirit of Compassion. It’s a point of no return where he must accept that he is A Real Person, and face some of the consequences of that (people see him, no do overs, bodily needs), and gain the benefits! (Agency, Learn and grow, people remember you, tasty food and silly hats)
But, as Solas is so quick to point out, The Spirit Compassion is gone. Replaced by Your Friend Cole.
So do you help Solas save Compassion and sacrifice Cole, or do you help Varric save Cole and sacrifice Compassion.
Like all good “Choose which companion lives” I personally don’t think either option is wrong.
(Noting here that talking about him is confusing because there is Cole (the mage boy) and Cole (your friend) who are distinct. There’s also Compassion (capital C , it’s a name) and compassion (lower case c, it’s a word).