It doesn't change the intent of the game. The intent is to successfully round the bases. You can't do that when the other team has full control of the ball as its way too easy to throw you out. Batting serves the purpose of momentarily removing control of the ball from the team in the field. A wild pitch also serves that purpose, which is why runners can run on such a pitch.

I don't believe it would be a fundamental change to allow even the batter to advance on a wild pitch.