Think of Porkin's death in Star Wars, Tasha Yar's death in TNG, or Vedek Bareil's death in DS9. All of these are examples of characters with limited screen time with still impactful deaths. Tasha we knew the most about, but even so, she was rather one dimensional at the time of her death--usually relegated to "yes, captain" and "Hailing frequencies open, sir." Some of these deaths go quickly and some are lingered upon, but in these cases, it is not just the character's death that creates the drama, but how that character's death impacts the main cast around him/her.The writers are instead putting in these emotional payoff scenes without the buildup or development necessary for those scenes. Think of scenes like Picard joining his crew for poker, Sam's "I can carry you, Mr Frodo", The Red Wedding, Han Solo's death, "The Body" episode of Buffy, etc.
I also think that the letter writing scene wasn't necessarily about any individual character, but rather showing how going into a bad situation impacts the crew as a whole. To me, this scene and the scene in which Discovery are being abandoned resonated in a way similar to Picard walking the Enterprise D right before the confrontation with the Borg in BoBW. Both are nice character moments, but what's more, both illustrate the emotions of the fear/anticipation of knowingly walking into a potentially deadly and/or life changing situation.