The is no possible death scene for Kirk that people would accept.
The only acceptable way Kirk could have been killed off would have been to go the full blown operatic scale of sacrificing himself in a massive explosion to save the Enterprise and the entire universe. And there's the OMG moment as the surviving crew witness from a distance.
Sort of like "The Doomsday Machine" on a $100 million budget.
And if he always knew he'd die alone, not even we the audience should actually see it up close. That leaves us free to imagine what those last seconds could have been like for him.
And even then the reason why Kirk has to kill himself at all would be a stupid one.
"Autopilot offline", "Transporter offline" and other bullcrapshitfuck.