Yes, handwriting is still necessary.
Tom Berger at Edutopia:
What We Lose With the Decline of Cursive
Technology is gradually replacing cursive instruction—but have we taken stock of what we’re losing?
Proponents of the script clearly don’t think so. In the case of cursive—and more broadly, handwriting in general—there’s plenty of evidence of cognitive and academic benefits. Brain scans reveal neural circuitry lighting up when young children first print letters and then read them. The same effect is not apparent when the letters are typed or traced. Intriguingly, according to reporting in The New York Times, “block printing, cursive, and typing each elicit distinctive neurological patterns,” implying a deep, underlying sensitivity in the brain to even minor changes in the way letters are rendered on the page. When reading and writing, we appear to be hardwired for versatility.
Personally I like the Barchowsky method.