So now you have just created a many-to-many relationship. Due to a bug in software, a child could now be linked to multiple parents, or even no parents. Part of good database design is preventing corruption of these sorts of relationships.

> I think it's more about the expressivity of pointers and arrays compared to the "backwardness-feeling" of index lookups.

Greater expressivity in ways to store bad data is never a good thing.

Huh? If you have a tree with parent pointing to children, how do you get a child's parent? You need an index. Same as with a DB.