Two pages late on my response to this, but here it goes anyways.
Can we, though? Last I checked even at the peak of our destructive capability -- which we're not really at anymore -- we couldn't really manage that. Destroy human civilization, sure, wreck huge chunks of the biosphere, definitely, but destroy anything on the surface? Is shit out there that takes more than a sustained nuclear bombardment to get rid of. Honestly, our best bet is probably what we're doing environment wise, and even the worst of that is unlikely to surpass previous mass extinction events.
We're pretty damn good, but we're not that far, yet. We've still got a ways to go before we really can even really top a sustained wide-scale algae bloom, and when you're being outperformed by pond scum, you don't get to claim superiority
I did some calculations a handful of months back and came to the conclusion that at our height (and still today) we have the cumulative destructive capability to basically destroy
anything on the earth's surface. However it's important to recognize that while we can destroy
anything, what we cannot do is destroy
everything. Even at our height of nuclear destruction we would have been hard pressed to simply cover 20-30% of the earth's land area (funnily enough about the same as a very rough estimate of how much of the land area we actually use) in non-overlapping nuclear devastation, and nowdays we can probably only hit somewhere between 10-15% of the total land area, based on the accuracy of various estimates about current stockpiles.
(It's also important to realize that in the case of trying to destroy certain things [such as say, mountain ranges], we would be much better off planting our bombs
inside of the mountains like we were blasting rather than trying to devastate it with a top down bombardment.