Part of the situation is due to an ambiguity in "cursive". It can mean either any fast-written script, or a particular formal style of writing. We really could do with disambiguating cursives defined by joins, and those defined by letter form. For instance, my handwriting on an informal note uses (mostly) "print" letter forms, but joins them up. To a calligrapher, it's a cursive (quick and scruffy). To someone for whom "cursive" is the neat handwriting your teachers tried to drum into you, it's print. In many cases "cursive" in the second use is coming to mean a book-hand, a script reserved for formal documents, the exact opposite of the original meaning.

And no, I don't think second meaning "cursive" documents will become indecipherable, although it may require practice to get your eye in, rather like reading most historical hands does nowadays.