I disagree. The 9th inning can have special significance, and not just for fans, depending on the closeness of the game. The difference between the 9th inning of a 1-run game, and the 6th inning of a 1-run game, is measured by the difference in win probability and 'leverage'. Statistically, a team has significantly less chance of winning a game they trail by one run in the 9th vs. a game they trail by one run in the 6th.
So statistically the 9th is indeed special. The real question, presumably, is how this affects the pitcher who has to pitch the 9th vs. the pitcher who has to pitch the 6th.
And the only people can answer this are the people who actually do it.