Can anyone tell me is it a wise choice to write an additional why essay for schools that do not ask for such essays.
I think it is quite an audacious thing to do! It can be good or bad. It is bad if you seem like you just had to write a why essay for other schools and included it just for the heck of it. It is good if you make a big deal of the fact that you wanted to express WHY you wanted to do there but were dismayed to see that no such essay was required. How impressive it is to impose an additional requirement on yourself! :-)
You write very well, but I want to know WHY it is essential for you to go to this school instead of some other school. What makes this school best for you? Convince them that they must let you into this school in order for you to proceed on a methodical and brilliant process toward your goals.