Rabbi Dov Landa opposes singing “Echad Yachid Umeyuchad” at weddings, and the like, comparing it to lofty “Shir Hakovod“, which may not be sung at random occasion and manner.
Via Toras Aba, I might have mentioned in this vein the Magen Avraham 565:5, as well. He says:
אין לומר האדרת והאמונה בצבור כי אם ביה”כ [ד”מ מהרי”ל].