Why is Bang! so predictable when I play it?
In some sense, your question is a bit circular. It's predictable because the games were all played with the same, predictable strategy. While it's definitely bad to start shooting away right at the beginning of the game, you don't have to save everything up for one final shootout.

If you're an outlaw, you don't have to just shoot at the sheriff - killing a deputy or renegade is good too, and you can potentially go for that without demonstrating that you're an outlaw. If you're a deputy or the sheriff, you don't have to wait until you know who your target is - in fact, if you wait until people are shooting at the sheriff, it's probably too late. For the deputy and sheriff, most other players are valid targets, so even if they shoot someone without knowing, more likely than not it's someone they wanted to shoot. 

For many players, it's advantageous to weaken the players between them and the sheriff. For the outlaws, this is good so that they'll be within range of the sheriff when the time comes, and for the deputy, it's good to have the sheriff on one side and reduce the number of hostile players they're within range of.

And this brings us to your assertion that there's no information. Once people are taking potshots, there's a little bit of information - everyone's trying to eke out a bit of advantage before the late game without putting all their cards on the table. It's still not the deepest game, but it doesn't have to be as dull as the way you've played it.