Why doesn't Captain Kirk have PTSD?

There is not a one for one correlation between seeing multiple deaths and suffering from PTSD.

Those prepared for the stress of a traumatic event are less likely to have PTSD. Also, people with a lot of social support tend to recover from stress and not get PTSD.

And lastly, one factor in experiencing PTSD in a military or disaster situation is recognizing the humanity of the enemy or the victims one is helping.

Kirk on the other hand would not ascribe humanity to most of his enemies, especially Klingons. But he recognizes the humanity in Vulcans, which is why he grieves for Spock.

Who says he doesn’t? A lot of his decisions seem erratic and illogical, and his relationships are tumultuous even with his best friends. And in episodes like Errand of Mercy we can see Kirk’s bloodthirstiness and rage come out, where he’s furious that the Organians prevent him from going to war with the Klingons. On the surface Kirk is reasonably functional, but that’s probably because of the advanced psychiatric techniques available to Starfleet. Remember that he has to take not only regular physicals but regular psychiatric evaluations, and that he can be removed from command by the medical officer if necessary. While I suspect Kirk is severely damaged inside (the planet which grants people wishes for entertainment results in Kirk having a brutally violent fistfight with an upperclassman he had hated from Starfleet Academy named Finnegan for example), he is able to keep it largely repressed.

@SmashTheState excellent diagnosis.

Because he’s so awesome.

Because he is an actor?