Deeper processing isn't necessarily better. I would bet it also takes "deeper processing" to learn all the characters in written Chinese. There's been movements to simplify Chinese, but never movements to complicate English.

Language is best when it uses as little processing as possible. Its meant to be a medium, not a mental task in its own right.

So taking your research claims at face value, that's not actually evidence that cursive is good. In fact, its the opposite.