Why to normalize an adjacency matrix?

Question

In Kipf & Welling (2017) paper https://arxiv.org/pdf/1609.02907.pdf. It uses the normalized adjacency matrix $\mathbf{A}_{symm} = \mathbf{D}^{-1/2}\mathbf{A}\mathbf{D}^{-1/2}$. I know the largest eigenvalue of $\mathbf{A}_{symm} = 1$. However, I still not very clear what the main purpose of normalizing an adjacency matrix is. Since an adjacency matrix does not include any feature information, unlike nodes. Without normalizing it, it should not affect the model training, correct? Any explanation will be helpful. Many Thanks