I know I often kill people solving world problems by removing certain individuals
That's pretty cool, I am incapable of killing people in my dreams and I think most people are. It makes sense that stress at work would invade your dreams for sure. I think the only reason i analyze my dreams as much as I do is because it is a near nightly occurrence for me. Maybe I dream every night, I just don't remember all of them.
I think everyone has to dream in order to have a sound nights sleep. Your brain obviously never stops working as that would be worrying if it also went to sleep I suppose.