Do you feel that you have to be able to write anything to be a great writer?

That's pretty silly. It's just like saying the greatest musician has to play ALL instruments. If that were the case, YoYoMa and other amazing musicians would be too busy experimenting to focus and become masters at their chosen instrument. So I say, definately not. It's good to appreciate and become learned in all types of writing--reading poetry, short stories, essays, speeches, etc. will help you with your own writing. But the best writers focus on the type of writing they have fallen in love with. A bad writer is closeminded and says, "Well, I only write novels -- I think short stories are for lazy people." You should be open to the different types education-wise, but when you are actually writing it is best to master your favorite one.