Reply To: Relive Hakhel!

“since the Torah writes “lemaan””

See aforementioned sicha – footnote 17, for the difference between the lemaan of tefillin, tzitzis, etc. and the lemaan of Hakhel.

While kavana is necessary for Tefillin, it is not גוף המצוה, rather מתנאי המצוה, as opposed to תפלה.
See more at length in לקוטי שיחות חלק כב ע’ 116 ואילך. https://hebrewbooks.org/pdfpager.aspx?req=15952&st=&pgnum=130
See also בית אלקים להמבי”ט שער התפלה פ”ג.

[P.S. Again, I never looked into the dinim of writing. My rov has guided me to follow the Rebbe’s behavior in this case, and he would sign his chol hamoed letters with מפני קדושת המועד לא באתי עהח”ת, so that’s what I do as well.
But again, you are probably right that this does not apply to virtual writing]