If life expectancies rise fairly consistently across the population, then to a naive first approximation your life expectancy in and of itself does not effect the number of deaths you witness, since everyone else’s life expectancy rises, too, slowing down the rate of deaths in exact proportion to the extent that it prolongs your life. There are some tricky considerations related to the rate of rise, and the number of people alive at various times in your lifetime, but all in all I think life expectancy does not play much of a part or any part in this.

The only thing that really matters, then, is how many people you can come to know in any given time unit. Here I tend to agree with you that we’ll just adapt. And beyond that, I don’t think everyone’s going to know so many more people, as Kottke supposes, unless our brains change in deep and fundamental ways. I think celebrity will tend to become a more field-specific thing, instead of having geographic boundaries. Increasingly, rather than something or someone being, say, “big in Japan”, someone will be known to a worldwide community of fans of, say, bunraku, who meet and communicate virtually. I think there’s something paradoxical about supposing, as Kottke does, that we will all reach the point where nearly every day someone whose work had a huge influence on our lives, and whom we would mourn, dies.
In an adult lifetime of, say over 26,000 days, that would imply 26,000 people dying. Over the course of your life, let’s suppose that most of the people who you are influenced by are older than you, but a good fraction — say 1/3 — are younger. So this adds up to at least 39,000 living people who influence you in a deep and personal way, such that you would mourn them. That means you experience about 1.5 deep, personal influences every day of your life.

Is it really feasible that there could be many tens of thousands of huge conscious influences on your life, that you actively thought about and treasured from that point onward? That you could forge one and a half such connections every day of your life? At what point do those influences become not so huge by virtue of being just one among so many others? Can people even remember the names of 39,000 people, much less identify some important work that each of those 39,000 living people performed that directly, consciously influenced them? That just doesn’t add up for me. Hundreds of important conscious influences — ok. Thousands — ok, for thoughtful people with a lot of free time. Tens of thousands? I don’t believe people as we are today are capable of absorbing that much influence in a deep, meaningful way, such that we feel personally touched by each of those people and carry around a vivid impression of them.

If it were possible, it would probably mean that human minds had changed in a deep and fundamental way, and thus would defy our speculation. In that case it’s possible to imagine an amazing medical breakthrough that effectively halts aging and all infectious or chronic disease, in which case deaths would become the rare results of accidents, murder, terrorism, etc.