At the most basic, it's hand/eye coordination.

Talk to any educator that's been teaching grade school children for a few decades. There's a definite lack of finer motor control in children that haven't been taught to write in cursive. That is one of the reasons that I keep seeing as an example when it's brought up for consideration to be reinstated. (this is ancillary to the whole skilled craftsman/labor pivot that is finally being addressed!) Hand skills do make a difference.

NGL, my husband can't write in cursive and his printing and other finer motor skills are shit. He cooks and I fix the cars and the electronics and help him with whatever projects that require nimble dexterity. I also have a bang up easy to read handwriting script AND can print like an engineer or draftsman. Both my parents made sure I could write cursive and print legibly. Mercilessly so..