My handwriting is so bad, that after I die it will be a collectors item as abstract art!!!
Cursive writing, and writing in particular is still taught regularly in India.
In India, students write by hand in their notebooks as well as in their answer papers. I am not aware of how things happen in US.
Cursive is definitely faster (though some feel otherwise). By "printing" I take it you mean writing individual alphabets, probably in upper case.
I feel writing is important to knowing and preserving the language and aids in communication. No wonder we have UseRealWords !
Imagine the Rosetta stone with "texted" words! What a confusion it might have caused!
A beautifully written document, beautiful as in handwriting not necessarily content, is a piece of art. I personally absolutely love the "copper plate" style.