I think the distinction with cursive is that all the letters in a word are joined, whereas with normal joined up writing some joins (particularly with letters like s, j and g where you have to cross back over the letter) are omitted.
I don't have a lot of patience for cursive writing, so I certainly wouldn't want to see it emphasized in schools. It is highly arguable whether it is faster (in practice a mixture of joined letters and printed seems faster rather than including superfluous loops), and as to legibility I invariably find cursive writing worse. Frequently it is very neatly illegible, but that still makes it useless with the exception of its use as a signature.
As to calligraphy, while it's a nice artform, I don't see any need to emphasize it more than, for example, origami. Neatness is not the function of handwriting, and far too often legibility is sacrificed for it. In any case it is becoming increasingly true that anything where neatness is required should be typed.