It's definitely not faster to write. That's kind of the whole point. Also it's barely a "different" system. You just join the letters together. In the UK it's called "joined-up writing" and everyone learns it in primary school where there is plenty of time for learning.

It is definitely easier to read print though - for a lot of people's handwriting anyway. It's much easier to be lazy and just do an illegible scrawl with joined-up writing than print.

It varies a lot though; I had a PhD supervisor whose handwriting was illegible to everyone - even himself! My wife's handwriting on the other hand is practically a font.

Print is just so slow to write...