You know how almost every Straw Hat Pirate and their allies have tragic backstories, told through multiple episodes worth of flashbacks that unfortunately interrupt the main story itself and go on for too long? And you know how you could practically say the exact same thing about an adventuring party in a typical JRPG, e.g. Final Fantasy VII and Tales of Symphonia?
I know that they're to explain how certain characters act and behave the way they do, but I think they would have served a much better function than that. And that is to essentially contrast with them eventually developing social support systems with their friends or teammates during the main events of the story.
Usually, characters in anime have tragic backstories to make them more sympathetic and explain why they act the way they do. But usually, these characters grow and develop as such by forming social support systems with each other, not only to fight bad guys they can't fight alone, but also support each other even amidst whatever psychological trauma they experienced before the main events of the story. In the process, it slowly and incrementally sheds the grim, hopeless angst and reveal that there is still hope for them and the world around them, and that there will always be other heroes like them willing to support them, no matter what their tragic backstories are.
Which means that, if Shinji, Rei, and Asuka had tragic backstories of their very own like in Evangelion, and they developed a social support system out of each other and at least some of their supporting cast, and thus help each other get through the dark times, it would have created a small sense of hope and optimism even amidst the series' angst and tragedy. And unfortunately, Evangelion was created to be a deconstruction of mecha anime, which means that the three main EVA pilots and their supporting cast are supposed to be unpleasant and unlikable to each other, and eventually culminate in a controversial mindf*** downer ending to reflect the unpleasant, grimdark angst that made Evangelion such an iconic deconstruction of mecha in the first place.
And One Piece was meant to be the complete opposite. Even if the Straw Hat Pirates and their allies have tragic backstories, they still turn to each other as a series of support systems to help them get through the dark times, thus creating a sense of hope and optimism through the heroes' bonds of friendship with each other.