The issue is with that exact alphabet called cursive, and needing to be taught two distinct alphabets.
That's literally the part that people are saying we shouldn't do, because in huge parts of the US, that's what people mean when they talk about teaching cursive.
No one is saying to drop teaching handwriting. This entire thing is "teach one style of handwriting", ideally the one that can be used to address letters and matches what we use for every other form of printed media.
The point about the drawing was less that we should have kids do more art, and more that the specific orthographic tradition of cursive is unlikely to be required for the benefits. Normal handwriting is almost certainly sufficient.