Figuring out which plays work and which don't is an important part of preseason. Of course, preseason success does not guarantee regular season success, but you can at least find out which plays are *disastrously* bad. That doesn't help you if you are already pretty sure which plays you are going to use.
Another important part of preseason is developing young players. Last season, I was just trying to sneak through without getting people hurt. I didn't make it! Then I was happy with the shorter preseason. This season, I have some players whom I actually want to gain experience, so I want an extra preseason game for that. Otherwise I would have to sacrifice regular season games to give people experience I want them to have.
Avoiding injuries is a losing gamble. The extra game gives me more time to get over the injuries I'm going to have anyway. Experience has shown me that getting healthy is more important than avoiding injuries in the first place. If I can keep my nose above water, I can start getting people *back* at the end of the season, instead of losing them. There's no defense against that.