It's pretty simple. With base-stealing threats on base, a pitcher is likely to throw more fastballs since fastballs reach the plate quicker (and straighter) and gives the catcher a better chance at throwing out the opposing baserunner. In addition, many teams like to call pitchouts with basestealing threats on, which of course gives the batter a free ball, another natural advantage. Shortstops and second basemen have to cheat closer to the second base bag since they have less time to get there with a faster baserunner, either in a steal attempt or a double play situation, meaning there are more open holes on the left and/or right side of the infield. You're saying all these factors add up to give the batter an advantage, but they don't. The batter's preformance is virtually unaffected. You seem to make the same point as me in your first paragraph, and then make the opposite point in the second paragraph.