Halaivi said, “The Arizal said that the main point of the Tallis is covering the head.”
There is a Gemara in Kiddushin, about Daf 30, that says that wearing a certain head covering up on the head is yuhara (showing off) if one is not married. That garment is interpreted to be a Talet Gadol.
I have seen yekke bachurim wear a hat with their TG. I beleive it’s because they don’t wear their TG over their heads.