That is very false. It’s kind of slow compared to handwriting print-looking letters (eg https://en.m.wikipedia.org/wiki/D'Nealian)
Source: https://theproductiveengineer.net/is-it-faster-to-write-in-c...
And also for many years I wrote cursive, then I switched to something that looks like D’Neal, and it was somewhat faster and easier to read (but not super fast)
The origins of the cursive method are associated with practical
advantages of writing speed and infrequent pen-lifting to
accommodate the limitations of the quill. Quills are fragile,
easily broken, and will spatter unless used properly. They also
run out of ink faster than most contemporary writing utensils. [1]
I handwrite with a modified semi-linked italic cursive. It's about twice as fast as my printing, and I can go faster, if I let it turn into a scrawl. That can't be done with printing.
D'Nealian is intended as a teaching script, so the claim is dubious to me.
That said, I definitely don't write in stereotypical looped cursive. I remember that I did learn D'Nealian in school, and my handwriting today is something like a hybrid. The main improvement in speed for me came from the ability to write entire words in a single flowing hand motion, rather than having to pick up the pen repeatedly between letters. Cursive provides a consistent method for doing that.
I know that shorthand would decrease the time that I spend taking notes or would increase the quality of the notes.
Shorthand is something different.
[1] https://dlelegal.com/stenography-court-reporter-miami/
[2] https://planetdepos.com/trending/content/what-stenographer
Every time I've tried to change to print, however, I inevitably get stuck on the fact that I write like a child for months and months before any improvement can be seen. It's just very embarrassing to hand someone a note that looks like it was written by an elementary schooler who just learned their letters.
Why? Because I can't read chickenscratch cursive, but I can read print no matter how badly it is written.
Writing is fundamentally a communication medium, so if the resulting text is unreadable your writing does not serve its most important and fundamental purpose of conveying yourself to others.
As for how to improve: Slow down and write more. That's really all there is to it.