Kirk had to compartmentalize the death of his brother at the time- they were in a no-shit crisis. I'm sure he mourned later, in private and off-screen. Which is how it ought to work.
Mourned later after the crisis is over? Sure. In private? Sure. Off-screen? No. That's the sort of thing that ought to be part of the narrative.
In Disco mode, half the episode would have been taken up with him crying to Spock or Bones over his dead brother and barely able to function.
I don't know about "barely able to function," but having an episode with a subplot dedicated to Kirk grieving over his brother's loss would have been a
good thing. Grief is an intense, long-term experience. It's artistic dishonesty to portray it as something that you are torn up about for 120 seconds and then never deal with again. The very format of 1960s U.S. dramatic television prevented TOS from being artistically honest in its depiction of such events, and that's a shame. It prevented TOS from reaching the full heights of artistic accomplishment for which it had the potential.
For whatever it's worth, the
Crucible novel trilogy by David R. George III, published in 2006 for the 40th anniversary of
Star Trek, posited that after the deaths of Edith Keeler and his brother, one after the other, Kirk spent the entire rest of TOS in a state of chronic depression.
* * *
My crush on Jess Bush continues unabated. Chapel's scene with Spock was wonderful. And Celia Gooding is absolutely
delightful. She works to capture a bit of Nichelle Nichols's performance while bringing her own special something to the table as well, and she's given the opportunity to do more in one episode than Nichelle got the opportunity to do in twenty-five years of playing Uhura.
My only real complaint with "Children of the Comet" is that it falls prey to a bad habit the writers on DIS fall into fairly often -- having characters talk about their pasts instead of dramatizing it. I wish "Children of the Comet" had started with Uhura not quite being able to articulate why she wasn't sure if Starfleet was her long-term career goal, spent the episode intercutting with flashbacks to her life in Kenya, put the flashback to the loss of her family right before the "all is lost" moment, and then intercut scenes of her and Spock figuring out how to stop the comet from crashing into the planet with a flashback of her starting the process of moving on with her life and enrolling in the Academy, with an epilogue where she confesses what happened to her family to Spock and then ties in the resolution of the comet crisis with her starting to have resolution over her family's deaths. Show, don't tell.
In fairness, that might have been prohibitively expensive, since this episode was clearly a visual spectacle and they probably needed to minimize the need to construct new sets or shot on location after building the comet set and shooting on location in those desert sequences.