What does boundary discontinuity in DFT imply?
Because the left (top) edge of an image is unlikely to be a reflection of its right (bottom) edge, there are discontinuities all along the edges of an image when it is viewed as N-periodic. These discontinuities are represented in the frequency domain by high-frequency coefficients. From an image compression point of view, using the 2-D DFT as a transform would require to store these high frequency coefficients (or non-zero terms in the decomposition of the image as a sum of elementary components), which do not describe anything meaningful in the image itself, but are a nasty side-effect of an inappropriate choice of transform.