Comedy takes many different forms. Slapstick, Dark Comedy, Situational Comedy, physical comedy, ect. People don't need to do funny things for something to be hilarious.You did hear it's a comedy right? You've seen comedies before, right? People doing funny goofy things, sometimes in a work environment. I've heard actual police officers describe Brooklyn 99 as the most realistic cop show they've seen. It's a comedy with Adults doing silly goofy things because thats what real people do sometimes. SHOCKING!!!!!
Star Trek has always excelled at telling 'Situational Comedy' where the humor doesn't stem from in your face sight gags, but rather the natural ridiculousness of a situation. The Trouble With Tribbles is a good example of this since the story at face value is about dealing with a natural crises. What makes it funny is how one of the issues that causes this disaster happens to involve cute little pieces of carpet called Tribbles. I believed it.
LDS? I don't believe in it's humor being a natural fit for Star Trek. As a separate take on Star Trek that's not a part of canon? Sure. Like Adam West's Batman vs. Tim Burton's Batman. Two different takes on the main character, but they work on their own because they're not in the same universe. When they say this show actually occurs in the same Star Trek canon that's been around for 50 years, you're not adding to Star Trek. You're changing it to something that it is not.