Having a different avatar doesn't affect any paths. WiiSports would be very different if it didI think you've hit on the divide between two kinds of game players:
Those who want to play an interactive story
and
Those who want to interactively create their own story through pre-defined, "choose your own adventure" type branching paths.
Gaming has recently been heavily leaning towards the latter audience. I am firmly in the camp of the former. That said, I got some massive enjoyment out of seeing my DA:I Inquisitor and Mass Effect Shepard appear in cutscenes and start talking and being a person.
But It's not like Zelda is a narriative focused series anyway besides majoras mask