I haven't said anything about raid being incomplete just because the raid is easy on normal/heroic mode. I'm talking about the fact that they are incomplete because the bosses doesn't have all of their abilities in them. The difficulty of an encounter has nothing to do with it.
If a boss in normal mode had all of his abilities you could say that you have experienced the whole fight when you did it in normal mode.
But it's not the same picture since they contain different things. For your puzzle analogy to work the only difference between a mythic and a normal mode encounter would be the numbers, Boss HP, boss damage etc.
When in reality it's more like you are trying to piece together a puzzle but you can only complete the picture in mythic mode. When you do the puzzle in normal/heroic mode you will be missing pieces, making it impossible to get a complete picture.