Well, you wouldn't really be able to do that for the story world, as there would be players in various points of progress. They could do it in the PvP spaces as these would get reset for each round anyway.

In some areas, like tearing down trees or blowing chunks of boulders. But not in the scale of seeing the entire Vex citadel collapse on the battlefield.

I don't think it would be awesome or horrible. Where's the option for that? But seriously, I think it could work in pvp matches. It would have to be on a small scale though like being able to put holes in walls or whatever. The large scale of battlefield wouldn't be right for Destiny in my opinion. I can't see it working in the open world co-op part of the game though. I don't think it'll be implemented at all to be honest, but we'll just have to wait and see.

It might work with trees and rocks... Cause no one care about tree and rocks. It makes me sad

Destructible environments in a persistent multiplayer setting can be problematic because system resources, no matter how enhanced, are still finite. The simplest answer is that there is currently no system today that can permanently sustain a destructible environment on such a scale. Add to that the fact that such an environment inevitably would have a negative impact on the gameplay experience of future players who would not be able to interact with such environments, as they would have long since been flattened by previous players. MMOs & even a number of RPGs with destructible environments are not persistent, but will either reset after a time, or the destructible environment is contained within an instanced mission that resets upon completion & exit. Thus far, it has not been stated whether or not Destiny's play space is truly persistent. I suspect that it isn't, which is a shame, but understandable from a logistical perspective. If they did include destructible environments in the game, I suspect that they will be limited to instanced missions. A major example that occurs to me is that of the Colony Ships on their launch pads in Old Russia... Suppose one of your fellow players had managed to climb to the top of one of the launch platforms during their time on that map. Now suppose that, when [i][b]you[/b][/i] made your way to that map with the intention of doing the same, you encountered the Public Event wherein the Fallen ship jumped in, knocking those platforms over. If that playspace is truly persistent, you will no longer be able to have the same experience that your friend did. On the other hand, if those towers "reset" to their upright positions after a time, it could disrupt your immersive experience, seeing them magically fade into existence once more. Unfortunately, it's a tradeoff that's unavoidable when you're working with a public space in a multiplayer setting. You will eventually have one or the other.

Destructive environments. [i]Maybe. Though honestly it feels a little gimmicky.[/i] Dynamic environments (moving and changing elements) have been confirmed.

Maybe in designated areas. I just can't see it throughout the entire environment. But I could see some small shanty town on say Mars being a PVP zone and you and the rest of the teams can demolish it.