Are there any effects to destroying the stone statues in Bastion?

In Bastion, you will often come across stone statues of people. I've destroyed few I've already come across, however now I'm wondering what the consquences of destroying them are.

Do either destroying or not destroying the statues have any effect on gameplay?

The only effect you get is extra narration; there's no loot. You're not judged better for not knocking apart the stone/ash statues, either. In fact, the game encourages you to knock them down: there are a few plot points where you have to hit one of the figures to continue, and others where the narration builds on the story of the level when you do knock them down.