No, not cursive italic! I refer to the cursive that is in danger of disuse.
Recently I saw an image online of conventional cursive that was intended to demonstrate its value. A flaw came to my attention that said problem! All the letters within words were properly joined, but they did not consistently rest on the baseline. The sample was legible, but running off the baseline is one negative factor in the best legibility. As one follows the rule to join all letters within words it is common for hands to drag on the writing surface, pulling letters off the baseline and distorting shapes, size and slant.
In the old days students were taught to write with whole arm motion. Only the ring and little finger rode along the writing surface. That is not a common posture now, and more of the writing movement is in the hand.
Italic does not really lift the hand between letters. Rather it drifts on and off the page, with letters that conform best to natural movements of the hand and fingers. The movements are rhythmic to keep writing on the baseline even when the paper is unlined.
All this should be considered when a school or parent selects a handwriting program.