I kinda get your point.

I always saw the "how I became the greatest hero" as him surpassing All Might. Not only in strength, but as a character.

All Might is a basic fighter. Izuku learns how to be a more complex fighter.

All Might has a basic view of the villains. Izuku begins to try to understand them.

All Might carry the world on his back. Izuku is willing to share that burden with his friends.

All Might want to do things alone. Izuku is accepting help from his friends.

Izuku saying "we became the greatest heroes" puts all the characters in the same box. And I understand that thematically the "I" means Izuku carries the world on his back alone and the "we" means he shares that burden with his friends. But I think could have been done better.

I think a way to do this would be to have the characters say their goals before Izuku says "we became the greatest heroes".

Izuku: This is the story of how...

Class 1-A: became the Number 1 (Bakugo), make my brother proud (Iida), help my family (Todoroki), help my parents and save the heroes who are hurting (Ochako), etc.

Izuku: we all became the greatest heroes.

It would still have the thematic idea of Izuku sharing his burden with his friend, but also makes it look that while Izuku is becoming the greatest hero by doing that, the other characters would "become the greatest hero" when they achieve their personal goals.