“No tefillin on Chol Hamoed is a tosafos.”
The idea is in a tosfos in menachos, yes, but they don’t seem to actually be talking l’maaseh.
Anyway, I still don’t get your point. You seem to want this to be a Chabad vs. everyone else issue, but it’s so not. Rov ashkenazim don’t wrap on chol hamoed either nowadays.