It would seem to me that this is one of the most popular lyrics in the world, right up there alongside "Baby, baby, baby". I always smile when I hear it, just because I feel like nobody else notices how much it's used.

Why is it so popular? It rhymes well (fight, light, bright, might, flight, height, white, kite, plight, etc.); it can be used in so many different flavours ({it all/everything/you/we/he/she/they/boy, you/girl, you} + {will/are gonna/just might/will always be} + {alright/OK/just fine/wonderful}); it is simple, so it can be used as lyrical filler; and it is vague, so it can be used at almost any time without being incongruous with other lyrics.
I think, though, that the main reason why it is popular is that we want to believe it. Since the dawn of time there has always been danger around the corner, whether it be terrorism or the Bubonic Plague, and people feel understandibly comforted by the thought that all will be better one day. It's like a tiny religion that's encapsulated within just a few words.