Why zig zag manner scan is used in DCT for image compression?
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.