While I'd say your points are mostly... on... point, I'd disagree that pieces have different value in a concrete way.
Any piece's value at any given time is directly related to how much it contributes to protecting your king, attacking the opponent's king, or both. At the start, your pawns are worthless by this measure; however, further on in the game, they can be instrumental in limiting an opponent's movements and avoiding potential check situations. But that value, and all other pieces' value, are constantly in flux -- and your opponent's attempt to figure out which are the most valuable pieces to you is the process of trying to read a player's next few moves.
Which I think speaks to Greg Karber's opinion above: The king's importance creates the central goal and drama of the game.