I think the main point being conveyed is that writing by hand improves recollection. Whether it comes naturally or not, or whether it is a better system or not, of course is subjective. However there is truth in the notion.
When I draw something I can remember the shapes better than if I simply sit there and stare at it. Something with the hand-eye coordination triggers the brain into remembering.
Typing in contrast, one is not tracing the shapes of the letters (the thing to remember), but pushing buttons that are not physically related.
It’s the same thing as if you can touch and hold an object it becomes much more real than if you can see it in a picture or on a screen. Remembering is connected better to touch.
Yes, writing by hand is an experience that offers unique benefits. The physical act helps to consolidate and integrate knowledge — improving recollection is one benefit, although I'd emphasize improving intuition as more valuable.
The primary activity of note-taking is forming words and grappling with ideas, though — it's not like all benefits are lost when using a keyboard. To a certain extent other activities like typesetting achieve similar ends.
My brother writes novels longhand, and I've thought hard about this topic. Ultimately, certain personality quirks held me back and I never felt carefree when hand-writing notes. Version control liberated me.
One of the benefits I've found is that it forces me to be brief. I've almost always kept notes and journals in a text format that I store in VCS, but I've found that journaling by hand is a vastly superior experience. It isn't simply about writing. It's about thinking of ways to write what I want more tersely (I'm prone to being verbose), and it's helped me process things ex post facto in ways that writing out the way I used to do simply couldn't accomplish.
I've also started collecting fountain pens, so it's linked to a related hobby. It's difficult to express that it is the entire experience, from the ink, to the feel of the pen, to what words are being written onto paper, that feels the most rewarding. I've also rather deliberately avoided document inks after much contemplation. I figure that the majority of inks I have aren't waterproof; if the journals ever get wet, everything in them will be destroyed.
That's how I've grappled with the ephemeral nature of the physical. Rather than aiming for optimizing permanence, as best as can be done on tangible, material books, I've preferred to embrace its weaknesses with full acceptance of what can (and will) go wrong. I suspect this is also because I have very little intent to ever go back and read what I've written. That could change, of course.