See, I have always considered that it had the opposite effect - by looking at the big picture, putting things in perspective and calling for a more humanistic outlook on life, it inspires empathy and action towards "making the world a better place". Far from trivializing widespread issues such as the ones you pointed out.
But then again, you already acknowledged this out in your previous comment, and I get that here you were just trying to explain what you thought the alternative was.
This is how I take it too. Sagan isn't saying that all human problems are insignificant or unimportant, but it's entirely true that many of the things we fight over and even kill each other over are, when put into perspective, pretty stupid. The whole point is to take a step back and carefully evaluate things as a first course of action and to try to save conflict and aggression for situations where it's meaningful and likely to make a positive impact in the bigger picture.
But then again, you already acknowledged this out in your previous comment, and I get that here you were just trying to explain what you thought the alternative was.