Yes, because if the world is all war, hate, and pain, then their is nothing to look forward to. Colors, joy, and love were made to balance that all out.
Yes, experiencing colours, joy and love are worth experiencing pain, war and hate, because life is all about love, happiness and pain as well. Pain and hatred teach us to get stronger and move on. If we only experienced happiness then it wouldn't have taught us to move on with things. At the end of the day, everything is worth it.