Why zig zag manner scan is used in DCT for image compression? I am not sure why zig zag manner scan is used in DCT. I can guess that might because it moves from low frequency component to high frequency component and as most of the energy is stored in low frequency component that's why this way of scan is favored but not quite sure.
You are right! When it comes to quantization, bit allocation or issues like that scanning in zig zag manner seems to be most efficient. 

As you said, (and I emphasize) in Natural Signals, lower frequency coefficients contain most of the energy. In a DCT matrix, as you go along a row the frequency is increasing in the first dimension and as you go along a column the frequency is increasing in the second dimension. A high frequency in any dimension probably contains less energy. So for example the 
$(2,2)$ entry in an $8\times 8$ DCT matrix $\bf{usually}$ contains more energy than the entry $(1,8)$ in the same matrix.