I don't think the show "should" show any position due to rank or title and I agree that Discovery wants to be all about a specific subset of the crew regardless of their rank or position. What I object to is what eschaton pointed out above: the show wants to focus on character X, so it contrives a reason (or just jumps to that character for no reason) to get them involved. Or, for no reason ignores the logical character who should be involved in the situation. Why have Burnham leave the bridge twice without identifying her XO? There was a whole storyline last season dedicated to trying to find one. Why leave the role heavily implied but not stated? That is the perfect, in story, reason to highlight it. That is the perfect time to give whatever character who was chosen last year their moment in the spotlight - to bask in a moment where we see who was deemed worthy to be second in command. Why call to Stamets for an engineering solution? He isn't an engineer. He knows some stuff about engines and power systems because of his work with the Spore Drive, but he isn't probably even in the top 10% of crew on the ship in terms of general engineering knowledge. The sole reason he is involved in that scene is because he is a main character for the show. You wouldn't call up Culber for an engineering solution just because he is a main character and hasn't gotten a scene recently.
If the show wants to have X character in a scene they need to 1) write problems for which that character already has the skill set or knowledge to solve or 2) show that character getting the skill or role for which you are writing these problems, either through training or promotion. The whole reason that Trek shows tend to involve the standard "classes" of characters (engineers, scientists, doctors, commanders, diplomats, etc.) is that the shows tend to write engineering, science, medical, leadership, or communications issues. It's the show being stuck using existing Trek tropes but not wanting to use the appropriate characters that causes the mismatch. If your chosen main characters (from a story perspective) don't have the skills or roles that allow them to logically solve the problems your writers are writing, you need to write different problems.