This is a complicated topic. I still remember the horrors of Elul in a certain very extreme Yeshiva.
Much as I vehemently disapprove of their approach the Rambam in Periush Mishnoyis does say that Rosh HaShana is a day of fear and trembling and not a happy day. Also, those Rebbeim and Masgichim were repeating what they heard from their Rebbeim and Masgichim who were Gedoloy Olam who knew Shas with Rishonim Baal Peh.
That said, listening to their smuzin alone you would not have known that Yomim Noriam are days of Rachmim, you would not have known about being Mamlich HKB’H on Rosh HaShana. Had their Rebbeim been speaking to people like me they would not have said such things and would have emphasized other parts of Rosh Hashana as well/instead.