While that is probably an accurate analysis, it has nothing to do with Kratz's gzeiros. I know him well enough to say that it was probably someone else's idea.
The gabai in 770 in the תש's decided that for kavod hatzibor you have to wear a tallis in the main Minyan (just like many shuls around the world)
Monday and Thursday the Rebbe was coming to a Bochurim's minyan, hence no Tallis.
Shabbos is a Baalei Batim minyan, hence it's kovod hatzibur that even a bochur would wear a Tallis.
In ל"ח mendelbaum was the בעל קורא for a few weeks in the main minyan and he wore a tallis