Q. Some shuls have a custom that the Baal Shacharis on Rosh HaShana & Yom Kippur sings HaMelech from his seat in shul instead of at the Amud. What is the source of this custom?

A. A. Horav Shlomo Miller’s Shlit’a opinion is that on the Yomim Noroim we are requested to be “machriz,” proclaim and assert that Hashem is king. Therefore, we do it in a more explicit and expressive way.
Horav Ribiat quoted from seforim that explain that the Talmud (Gittin 56b) relates that when Vespasian demanded from Rabi Yochanan ben Zakai; “If you insist that I am the king,why then did you not come until now?” Therefore, the shaliach tzibur proclaims that Hashem is king, as soon as he begins his service, even before he reaches the amud.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a