All other exercises would need more expensive tools and after inventing a sufficient number of different patterns for other activities, that would be practically equivalent with writing a different alphabet on another medium than paper, e.g. carving wood or stone, etc.

I did not like to use handwriting for things like taking notes at school or at the university, and I switched to typewriting as soon as I could afford a computer. For work purposes I now use only typewriting.

Despite this, I am very grateful that in the first years of school I was forced to practice handwriting, even if I have abandoned decades ago the style of handwriting that I was taught.

The reason is exactly what the previous poster has said, that this practice of handwriting as a child was essential for developing the motor control that I needed later as an electronics engineer for soldering or for assembling and disassembling various miniature devices.

for one it's not clear to that this is what is actually important in writing or unrelated. That's just a bias in a culture that systematically neglects embodied practice.

In Japan there's an increasing phenomenon of Kanji-illiteracy among the young. Turns out there is a close connection between writing them out, the order of strokes and the physical activity and the memorizing of meaning of the Kanji, just passive observation or digital input can't replicate. There's a reason calligraphy is such an important tradition. There's an inherent connection from your hand, to your working memory to the processing of symbolic meaning.

This mirrors the discourse you see in math. "Rote memorization, writing equations, isn't important, you need to be able to think" turns out it really isn't and countries that teach traditionally excel at math. We live in an educational culture of thinking-pilled people who disregard the physical world and practice with abysmal results.