That is what I assumed for a long time, but career path studies have shown that the average pitcher declines faster than the average hitter. This might be explained by your second point that pitchers are more likely to get injured. At any rate, I would bet that the confidence interval around career paths for pitchers is a lot wider. Pitchers may decline faster, but it is possible for them to avoid decline by getting wiser with age. There is not much a hitter can do once they lose their ability to react.