*SPOILERS FOR THIS BOOK AND OTHER HP BOOKS*
You know how Harry peeked into the pensieve and saw his father giving his O.W.Ls with Sirius, Remus, and Snape sitting around him, the memory where he saw how much his teen father looked like him, the memory where, unfortunately, he also saw James and Sirius bullying Snape, where and when his idea of having a flawless father was shattered, where he learned that his father hexed people for fun, where he witnessed his father's arrogance and how it affected other people?
Imagine Harry's children manage to peek into Harry's memories somehow too. But instead of witnessing their father and his friends bullying others or having a laugh on someone else's misery, they witness the beautiful friendship of Harry, Ron, and Hermione, who were always up to accepting the misfits. They see their father taking Luna to the Slug Party instead of bullying her because of her eccentricity, they see him not levitating Dean because he was dating his crush, they see Hermione always helping Neville in his troubles and not hexing him for fun despite being the cleverest witch, they see the trio standing up to Draco's bitterness, but never crossing the line for pleasure. The kids see that despite being in trouble and fighting odds at all times, they were always softer and warmer towards other students. They see the trio sitting under the Beech tree at the edge of the lake not laughing on someone's misery, but laughing among themselves or on a self-deprecating joke that Ron had cracked. Imagine what a marvelous learning experience this could be for Harry's kids.
I always wonder this when I read this book. I love reading about the Marauders, because they all have very powerful and interesting personalities, but Harry, Ron, and Hermione's friendship made them better people.