While I am not a fan of this guys opening monologue (As not every tribal song sounds the same, it's not a lion king song, it's a traditional folk song sung by the sami) I do agree that olaf is vital to the story. More so than other comedic relief characters that Disney has had in their films. More important than anna? No. But important none the less. In fact I would argue that his role as a comedic relief character is far more pivotal than anything Disney has done with that type of role. To me I see Olaf as the actual embodiment of Elsa's Love for her sister.
Let me explain from the beginning of Olaf I guess. Elsa's love for anna takes shape during let it go, the first thing she makes when she starts unleashing her powers is a snowman. The snowman her sister desperately wanted her to make. The thoughts going through her head when making olaf must have been of Anna and her childhood (which is why its olaf and not some other snowman like marshmallow). She put the memories of the love and laughter she shared with her sister that night into that little snowman which helps shape olaf into well olaf. More evidence to that is the fact that is when looking at the northern lights Olaf says the same thing Anna said to Elsa the night they both went to play as kids for their last time “Look sven the sky is awake”. Olaf turned out happy and nice and wonderful due to the motive behind making him. Which was Elsa wanting to do what she always wanted to do with her sister, the memory of the happiness they had shaped him. While marshmallow is bulky and aggressive and rather rough due to Elsa making him out of a need to isolate herself and being scared and angry all at once while creating him.
So soon after let it go Anna is alone with a stranger on a mountain and they both need help, who do they bump into? Olaf. He could have turned around and went with Elsa to her new palace, but he didn’t. Somehow found his way to the one person who seriously needed him. So he bumps into anna and is immediately caring, gentle, and friendly with her. Then he meets the male stranger Kristoff and not only gives him attitude, but pokes fun at him as well (much like an overprotective sibling would when meeting anyone who could be interested in their younger sibling). The whole time he keeps kinda giving Kristoff the attitude while he does nothing but love and protect anna. He is so quick to call Kristoff out too whenever he might offend anna (again much like an overprotective sibling). For example when anna’s hair turns white and kristoff is weird about it the first person to call him out on it is Olaf “You hesitated”. Which is his way of telling kristoff she is perfect and wonderful because she IS EVEN WITH WHITE HAIR that is my little sister punk let her know she is perfect and wonderful (okay not really but in essence lol). Even when they go to meet the trolls and he suspects kristoff is crazy his words to Anna are “Anna because I love you, I insist that you run”. He again will take the bullet for her so long that she is safe, his concern is for Anna, not Kristoff.
Olaf is basically looking out for Anna on Elsa’s behalf. He is the one who finds Anna locked away and freezing to death, where once again he takes care of her and indirectly tells her what Elsa has been doing for Anna since day one. “True love is putting someone else’s needs ahead of your own”. He cares for her in that scene like a family member. Remember after Kristoff left Anna, Olaf could have gone away with him, but his priority was to be with Anna. In many ways he is the most dynamic “Side kick” character disney has ever done. Afterall if Elsa would have never “loved” Anna like some people say she would have never made him again, and Anna wouldn’t have had the chance to thaw her heart, or even find her sister.
Olaf is also a huge reminder for Elsa that she has the ability to not only create good in this world, but that love can set her free. When she sees what she made Olaf introduces himself and says “You built me, remember that?” and she looks at her hands in almost disbelief. Olaf helped Elsa realize she could do good things with her powers, she could do good things through love, specifically through her love for her sister.Which fits back into the ending when that realization fully hits her.
He is literally the embodiment of Elsa’s love for Anna. Everything Elsa would have done for Anna but couldn’t, he did in her place. Little guy is even willing to die for her, and after the two sisters finally reconnected he isn’t sad that he is going to melt. In fact he calls it the best day of his life, and most possibly the last. Because he was kind of made to bridge them back together and he managed to accomplish just that. He is Elsa’s love reaching out for her estranged sister and making things right again.
