I wouldn't want that, giving Link a background would ruin his entire purpose which is to be the connection between the game world and our world. They should do the opposite, remove as much backstory as possible and just make him a silent warrior whom we for gods sakes should be able to customize at the start of the game. Feels as if Nintendo both wants Link to serve as a connection and be his own character at the same time, which doesn't really work IMO. Even if they do decide to give him a background I won't be sad I'd just like for it to be well written and make sense with the plot obviously.
So either a completely empty shell which we can customize to fit us, or a story rich well written character.
This, basically. You're right, Link is meant to represent us throughout the game. I don't have a little sister named Aryll, or a best friend named Zelda, or an uncle who used to be a Hylian knight. Therefore, the connection between me and Link is cheapened because he clearly has what I don't. Link should be either a
complete character with background, established relationships, personal ambitions, and dialogue, or he should be absolutely nobody. The former approach makes him a full character. It makes him interesting on his own, someone we can get to know and respect. As absolutely nobody, we can fill in his shoes so easily with what we prefer. How did we wind up in Hyrule? We stumbled down a rabbit hole or something. But now we look like Link, and we're in a video game.
Currently, Link is hanging in the middle, but this is not a "best of both worlds" scenario. Link is neither a very interesting character nor a blank slate we can start on. This doesn't necessarily make him bad, but if Nintendo wants to improve their storytelling, they need to embrace one or the other. You can still develop your own ambitions and relationships as the story goes on. You can meet new people and witness remarkable events that affect you personally. You don't need an avatar with his own predetermined relationships and ambitions to do it.
Character customization is something that wouldn't be bad for The Legend of Zelda to try. Link's almost always limited to his green tunic, but what if you could outfit him with a huge variety of clothing and hairstyles to suit your tastes? Perhaps his green tunic could bear some special attribute that makes it preferable in certain situations, but I don't think it's really necessary. Developing your own character from scratch may be better suited to a spinoff, something that doesn't really affect the mainstream series. That way, Nintendo doesn't have to trouble itself with how that story alters the franchise. Still, aesthetic customization would be an interesting idea for the series to try.