The Wizard and I, to me, is the song that makes Wicked a tragedy most effectively.
Obviously other songs are important — No One Mourns the Wicked and the Finale reprise bookend the play, creating a full circle "doomed by the narrative" effect: the story and ending(s) are already written, and all you can do is watch, the intro ensuring that you know the ending from the offset in classic tragic fashion; No Good Deed is one of Elphaba's core turning points of losing the final vestiges of the starry-eyed girl she was in TW&I — but the Wizard and I stands out to me.
Part of this is because it is, in many ways, Elphaba's introduction. She's still a shadowy unknown figure, and while the movie fleshes out her childhood within the opening number to make it clear she was not always 'wicked,' in the stage play we only see being born as a literal (innocent) baby and nothing else: no hints of personality, no hints of kindness. When we do meet her on stage, she's often snappish and angry; on stage, TW&I is her great unveiling: this is who Elphaba actually is and wants to be, earnest and desperately wanting to belong, to matter. On screen, Cynthia's Elphaba is more reserved and resigned, dignified but always quietly disappointed; TW&I is her allowing herself to hope for things in a way that feels tangible and plausible for the first time in her entire life.
In either version, we have to understand how badly Elphaba wants to be with the Wizard: for status, for family, for love. Not only does it provide some very consistent characterization (to be his advisor is to be in service, which is what she ultimately offers to the Animals despite not materially benefitting from any of it, etc) but it also provides the basis for the rest of the play in so many ways. TW&I reaffirms over and over that she does want recognition/social affection, which is another crucial piece of her. It offers a parallel basis in her bond with Glinda ("She doesn't give a twig anyone thinks" "Of course she does. She just pretends not to") but also is the hinge upon which Defying Gravity turns. Because it's a song of empowerment, yes, but it's also a song of sacrifice: she is giving up many things in leaving, over and over again ("... what you've worked and waited for, You can have all you ever wanted" / "but if that's love, it comes at much too high a cost" and of course leaving Glinda behind).
Defying Gravity is the writing on the wall: despite being a song of triumph, there is nothing but sacrifice ahead. Elphaba is lonely, temped, and jaded throughout Act 2. And part of the reason we know this is because we know how the story ends, yes, but also because of TW&I wherein all of Elphaba's happiest wishes are undercut with cruel dramatic irony:
And I've just had a vision, almost like a prophecy
I know it sounds truly crazy
And true, the vision's hazy
But I swear, someday, there'll be
A celebration throughout Oz
That's all to do with me
And I'll stand there with the Wizard
Feeling the things I've never felt
And though I'd never show it
I'd be so happy I could melt
And so it will be for the rest of my life
And I'll want nothing else 'til I die
Held in such high esteem
When people see me, they will scream
We know, all throughout act 1 and act 2, that she doesn't ultimately stand a chance; Defying Gravity is the exception, not the rule. We know, in TW&I, that she thought she did. But in the end, she does not beat her own self-told prophecy despite trying everything she could to rise above others' views of her, to Be Good and be seen for who she is, to have some semblance of what she wanted as an earnest-eyed school girl. She defies death (and gravity), but she does not defy her Narrative.
And I think, at their core, that's what so many great tragedies are about.