It's about using your best reliever in the highest leverage situation, and about giving your team the best chance to win the game (best win probability). Because the 6th inning (and earlier) is still early in the game in comparison to the 7th, 8th, or 9th, it is not going to be as high leverage as the later innings, all other things being equal. What happens in the 6th inning does not have the same impact on win probability as the same thing happening in the 7th, 8th, or 9th innings.
To put it another way, if the opposing team went up by 2 runs in the first inning, their win probability would be much, much smaller than if that team went up by 2 runs in the 8th inning. The leverage of a situation takes into account the inning of the game.
Also, if the heart of the order is up in the 6th inning, they are guaranteed to get at least one more bat after that. If they come up in the 7th inning or later, and the relief ace can sit them down, they are not guaranteed to get another at bat in the game.