> "Don't be". What a silly way of wishing something not to be. It is a contraction of "do not be", which implies that the opposite is "do be", as if being were something one does.
> Previously I thought of this as natural English but now it's struck me as odd. Why can't it be "be not" or "ben't" or something?

"Be not sad" is perfectly legitimate English, but it's archaic and sounds lofty and Shakespearean to modern ears. "Take not the low road." "Spurn not the compassion of others." A lot of costume dramas have dialogue written in this manner -- often for the worse, because the composition of the dialogue distracts from the meaning of it, but certainly a lot of classic English literature is packed with these kinds of constructs.

In more modern English, the natural negative imperative of "to be" shifted along with all the other verbs. "Do not be sad," or "Don't be sad." "Do not take the low road." "Don't spurn the compassion of others." There's nothing special about "to be" here.

The positive version of this construct is also legitimate English and is used to make a command more emphatic. When spoken, a strong emphasis goes on the "do":

"Don't eat the plates. *Do* eat the food on them. Don't punch Mia. *Do* punch Stephen."

As for "do be," there are a few phrases with it that are used so commonly that the "do" isn't even emphasized. "Do be careful on those steps." "Oh, do be reasonable!" Though this is used in America, I tend to think of this construct as primarily the province of proper British gentlemen, which arguably suggests that this is the more elegant phrasing, even if it's no more or less correct.