I also noticed that Picard did not mention to others that he had help from Kirk to defeat Soran. I assume that this was because he violated the prime directive related to time travel. Could this be why there was no funeral for him? I'm sure that the federation has a cleanup or science crew that would come to dismantle or learn from Soran's invention and subsequently discover Kirk's body.
My intuition tells me that perhaps there was a disagreement during the development of the movie over whether Captain Kirk died or not, since there's no fanfare or funeral for such a legend, especially compared to Spock's grand exit. His death is not even confirmed, although many believe that it was his death. We see him in the scaffolding of the platform at the end, and that's it.
Also a curious tidbit: if Kirk did die, he did not die alone, as he stated in another star trek film that he would not die unless he was alone and therefore would not have others around to help. It would have been nice if all of the writing and lore of each movie had been carried on to the next one. I suppose that would have been hard with different writers though.