This is just thinking too much. Tony La Russa does it because he wants to have three hitters in front of Albert Pujols for greater RBI possibilities. In theory it might make sense, but really?
Why does a hitter in the NL bat eighth normally?
Answer: Because he’s usually a lousy hitter. Chances are he won’t get on base all that much for it to make a difference. The eight-nine hitters are most likely the team’s two weakest hitters, do does it really matter if the pitcher is eighth or ninth? Probably not.
If a manager wants to bat a hitter in the line-up where he’ll have potentially three batters (and three possible RBI opportunities) ahead of him, what’s wrong with clean-up?
And, batting fourth, you’ll have three better hitters and theoretically more RBI chances.
I’m missing something with the pitcher batting eighth.