What you call it has little influence on whether you do it well, poorly, or at all.
The problem in the US is not that we call it something other than "joined-up writing". The problem is that schools in the US no longer teach it.
My mother at 95 has beautiful handwriting. Her handwriting is so beautiful and consistent that she nearly had an application denied because the company thought her signatures (yes, plural; multi-page application) were a stamp or machine product. Only because an agent of the company was there and could affirm that he had watched her sign the application did they accept it. She calls what she does "cursive".
Note: my reply is based on my perception that tigger's comment refers to my #6, which was about the AE names for "Screibschrift" vs. the BE names. Tigger, if your comment referred to something else, it wasn't clear.
I do agree that students today print far more than they write longhand, and their cursive is often barely legible - and sometimes totally illegible. That's the result of lack of training and practice, not nomenclature.