I've commented on here several times that I'd like to see the pitcher batting 8th. This seems crazy, so I'll lay out my reasons.
1. The pitcher in the 9th spot is antiquated. It dates to a time when the starting pitcher went the entire game, and the goal was the minimize the at bats of the worst hitter in the lineup. But the pitcher rarely goes the entire game any more, so this reasoning is no longer fully valid.
2. The pitcher in the 9th spot makes it harder to score. How many times this year (in innings 1-6, because the pitcher is unlikely to hit after the 6th) have there been runners on, less than two outs, and the 8 spot in the order up? (AL rule games excluded). 45 times in 78 games played without the DH. That is just one situation where it would be preferable to have the pitcher (who can bunt the runner over) rather than the traditional 8th hitter. A runner on (especially in scoring position) with less than 2 outs should be a scoring chance. With the 8th hitter and the pitcher, in that order, it really isn't. With the pitcher and then a hitter, it becomes a bit more of one.
3. It's easier to clear the pitcher batting 8th. If the 8th hitter is up with nobody on and two outs, it would be better for it to be the pitcher. If the 8th hitter does get a hit, there is still basically no chance of scoring, because the pitcher is up next.
4. More RBI chances for the top of the order. With a hitter in the 9th spot, the top of the order would have a greater number of chances to drive runners in. Considering these are the better hitters, it makes sense to give them more chances.
5. With two outs and runners on base, the scoring chances aren't hurt anyway. We should be well aware of this; the reason why Cliff Pennington leads the team in intentional walks has nothing to do with his power. Didi Gregorius is tied for second in intentional walks. If there's a base available, the opposing team is going to pitch to the pitcher anyway. May as well just bat the pitcher in the 8th spot.
The reason why teams do not bat the pitcher in the 8th spot has to do more with player's comfort zones than with strategy. Batting behind the pitcher is deemed, unfairly, a mark of shame. Managers do not want to kill the confidence of their players by asking them to do so. Yet, it seems clear to me that it would be better from a strategic viewpoint. Perhaps it will take players volunteering to do so for the betterment of the team for a change to be made to this tradition.