You couldn't have that. There would be designed plays that would involve intentional wild pitches in order to get around pitching to a difficult batter. It would be no different than an intentional walk with the only difference being having an opportunity to throw the man out a first. It should remain as it is, with the batter only allowed to run after the third strike - at least in that instance the pitcher was forced to pitch and play the game, and did his job by getting three strikes. A batter is not like a runner on base. He's trying to get on base, as he is not counted as a man left on base when an inning ends.
Well, the batter wouldn't be obligated to run to 1st. Some batters would be at a disadvantage, but others would be happy to exploit the opportunity. Ichiro's at the plate, and the ball gets by Ivan Rodriguez. I'd love to see that one. :-)