because a shaliach tsibbur leads the services…that’s why. And if you hadn’t noticed ,in many chassidische sthieblech, they will insist that the shaliach tsibbur put the tallis over his head,even as the people might not do it. And again, covering one’s head (especially in a shul) has become the hallmark of jewish tradition even though it is a minhag.
“Puk mo amo diber’-just look at the events where a gentile is in the shul (check,for example, the recent induction of the British Chief rabbi and see prince charles with a yarmulka)and you will see what is the minhag.