I'm sure you don't have to but I don't see why you wouldn't use a major part of the game. Even if you play as a warrior, he/she is still dragon born as far as the story is concerned.
I guess, its just that i've never really liked using magic, not sure why exactly? just prefer to hit things with a nice sharp sword or whatever til they drop. If the shouts are essential to the story then maybe i will seek them out? just wanted to make sure that i could play without them,and not get stuck coz i didnt have one that was needed somewhere along the line.