As your sources explain, the practice of writing is important for learning. Through writing we develop thoughts, compose them, as fyngyrz says below, reformulate them. Writing is a way of thinking.
The issue, however, is not writing: it is handwriting. Typing, printing and cursive (I hesitate to include texting, as I find even swype/swiftkey excruciatingly slow, and I'm pretty sure using my thumb would bring on early arthritis) are all methods of writing. The links you include speak only of writing, not handwriting. They are not about the importance of cursive.
I strongly suspect that the different technical affordances of handwriting compared to typing do indeed lead to different learning experiences. One enables editing, the other demands sentences be formulated before they are written, and that subsequent words be adapted to what has already put down. Are such differences educationally significant?
One study found handwriting enhanced student composition more than did typing, though the authors put this down more to fluency (speed) and point to the importance of teaching touch-typing. This might actually support the Finnish position. Another article theorizes that there might be benefits to manual writing. A study of university student essay examinations found no difference in performance. This study found grade 6 students could type faster than they could write by hand.
This is just the result of a quick search, but I don't see strong evidence one way or the other.
Personally, my handwriting is awful. My teachers didn't even teach me how to hold a pen correctly (I have been unable to correct by habit of using all 5 fingers). Through university I took notes in my own simplified printing (each letter one stroke with at most one reversal), a system I still use when speed matters. Recently I learned that movement should come from the arm, not the wrist; for the first time, my handwriting became legible. Learning to type, however, felt like it opened up the world to me. I wish I could write fluent cursive. Is Finland doing the right thing? Darned if I know.