Bruggemann brought up that a reason we say this after the scripture is to affirm that the scripture is our story/text. It is the text which helps define and identify us as a community and a people. This is the Word above all other would be authoritative words in our world. Not the Constitution. Not the Bill of Rights. Not the philosophical thought of Marx or Locke or Dawkins or "the Market" or Plato or Rand. There are devotees of these sources which will elevate these authorities to demi-god status.
For the Christian to say, scripture is the Word of God is not only to say that these other sources are not authoritative in our lives, but it also says that these other sources are in fact not God.
*It is worth noting that we say the Word of God, and not the words of God. This public affirmation of the Scripture is not an affirmation of the idea that what was just read are the literal and specific words of God.