This is pseudo science.

How broadly the brain is activated is obviously not a meaningful measure of how well someone learns a topic. It is clear that handwriting requires more complex motor motions and visual processing, but why does that matter at all? Equivalently someone could argue, that, because more of the brain is "activated", the less focused the student is on the material, as the brain needs to perform additional motor and visual tasks.

>The study’s findings suggest that handwriting should remain an essential part of education

No, it doesn't. The setup could not even do it in theory. We lack a total understanding of how "learning a subject" and "brain activity" are related. There is no devices you can put on a human that could measure, after a study session, how well the human has learned some subject.

I hate these types of studies. Having a subject do something and measure how their brain lights up tells us precisely nothing. These studies are done again and again and again, there are no actionable results and no new insights. Nothing new about the brain was learned.

(BTW I wrote thousands of pages of hand written notes during University. My point has nothing to do with how effective or ineffective handwriting is for learning.)