Why do we use scaling factors in DCT? Are they important?
Scale factors ensure the normality of each DCT vector. Since the vectors are already orthogonal, factors are needed whenever the orthonormality of the DCT is needed (often compression, denoising). For visualization, comparison, feature extraction, scaling factors may be less important.

For operation efficiency, especially when integer arithmetic is used, the scaling factor can be incorporated afterward, in the quantization stage when used in compression.