In an interview with StarTrek.com, William Shatner admitted that he wishes he had stood up for his character when he saw how the captain was meant to be killed off, saying, "I would be much more courageous about suggesting, or demanding would be a better word, a more regal exit for this hero." He admitted that he didn't know the reasons why Kirk was given such an undignified death, but said that he really regretted not pushing harder to have the character's death changed. Given that Shatner already had to fight to change the ending once, perhaps he wasn't up to keep pushing to change the ending again after it had been revised.
In fact, according to a 2018 interview with TrekMovie, Shatner never even really wanted his character killed off, but felt like Paramount left him with no choice as they had decided to pass the baton for the "Star Trek" movies onto "The Next Generation" cast. Shatner was told that he could either appear in the movie and be killed off or, if he turned down the movie, they would simply kill his character offscreen instead. That exit for Kirk probably would have been even more unsatisfying for "Star Trek" fans than the shot-in-the-back sequence and the ending that made the final cut.