Pretty much all Zelda games have quirky, lovable NPCs that range from the cute to the downright creepy (yes, Poe Collector, I am looking at you). Breath of the Wild is no different. In fact, Hyrule's chock full of interesting characters, from ill-fated travelers constantly beset by Bokoblins to a Zora priest who wants to help people be happy in marriage.
But that's sort of where it ends. Apart from giving Link a quest or an item, they don't serve too much purpose, nor do they change over time as Link solves problems or makes headway in, y'know, saving the world.
It's a missed opportunity to really make something of all the effort put into creating interesting NPCs.
One thing it would be nice to see is how things change for them, especially if Link (and maybe Zelda?) help them out somehow earlier on. It doesn't have to make NPCs and their lives an additional plot, like some games do, but open world games thrive on dynamic characters and how they interact with the player.
Lurelin is a good example of why the game needs this change. It's a gorgeous, interesting coastal town, where absolutely nothing happens, and it could just as easily never exist.
Rather than leaving people with the same dialogue and circumstances regardless of what the player does, some of them should move around, actually reach their destinations, fulfill their goals — something, anything. Tarry Town gives us a taste of what that might be like, and it's one of the most rewarding sets of character interactions in the entire game (see the next section for more on that).
I lied when I mentioned Breath of the Wild already has the open-world part down pat, plus all the ingredients for those kinds of immersive interactions anyway, because there's actually one missing, crucial thing:
Tingle. We need Tingle.