This is why we've never seen or heard aliens out in the universe. Every civilization burns itself out faster than they can solve long distance space travel. Maybe the Great Filter is just the inherent nature of sentient beings. It would make me feel better to know that every other civilization to ever exist in the universe also destroyed itself in this manner, but maybe we are a special level of stupid.
We've been pretty up ourselves about it though, a blank flag waving on the moon will be cold comfort for the burning remains of our civilisation. I could imagine this being the inevitable end to an intelligent species, smart enough to destroy itself but dumb enough to destroy itself.