I'll try one more time to explain why this bothers me, although it veers into another issue - basically that the writers didn't know if they wanted a "small show" or a "big show" and so gave it characteristics of both.
In a lot of ways, Discovery was set up to be a tight drama centered on Micheal Burnham's character. This explains why much of the season is from her POV, we get a very limited view of the bridge, etc. The show could have been quite successful if it kept to the core cast of six and utilized their interactions to make interesting drama in a "small stakes" story. You could still have Micheal Burnham be a disgraced former XO who caused her commanding officer to die, and is seeking some sort of "redemption" in the Klingon War, for example.
Except, the series added all of these "epic" elements to the story as well to continually raise the stakes. Burnham was raised by Sarek, and is Spock's sister. She's the first "mutineer" in Starfleet history. Her captain was one of the most decorated in the fleet. Following her imprisonment, she ends up stationed on the most advanced ship in Starfleet. That ship develops a new type of drive which allows for instantaneous transit which has never been seen before. She personally kills the leaders of the Klingon Empire - twice. Both her Captain and her love interest turn out to be imposters. In the Mirror Universe, she ends up on the literal capitol ship of the Terran Empire (captained by a mirror version of her former commanding officer) and ends up taking part in a mission which not only saves the crew - not only the universe - but life in all universes everywhere.
All of these epic elements suggest an epic story - which means, among other things, loads and loads of characters. Game of Thrones in its first season for example had 19 main cast members and around 60 guest characters - in ten episodes! Obviously Game of Thrones has the largest budget in television right now, but Season 1 only cost around $6 million per episode. In terms of money, Discovery could afford a cast as wide as Game of Thrones. It also clearly has the run time available to flesh out that many characters.
The answer seems to be the stylistic muddle of the show - that it wants to simultaneously be a tightly-focused character drama and epic. I really find myself wishing it concentrated on the former rather than the latter however. If the characters are right, you don't need ridiculous "epic" moments.