Well, in a word, yes.
If you're trying to establish a world with rules, then when you just break those rules, it breaks the story.
You can say that you, personally, do not care. Okay, that's fine. But it's going to stick out like a sore thumb to anyone who has been watching Trek for a long time. You can do a series where none of the leads are in the chain of command. But you still need to have an actual chain of command on the ship. Otherwise it breaks the verisimilitude of the world.
Plus, it becomes monumentally clear that the Writer's are forcing Saru to choose Tilly and lose the ship because they want the audience to see Burnham as the better choice. That does not jibe with the Saru we've seen of previous seasons, or even that season. They're forcing him to make out of character choices to make the audience believe that Burnham is the better captain.