Funerals aren't meant for the deceased, they allow the living to mourn and move on.
It may be irrational fears, but living people often fear what's gonna happen to them after they die, and respect for people extends after they die for most people. Not for everyone, but this means that some will feel uncomfortable about sharing private stuff. And then there's also superstition.
Speaking only for myself, it has been invaluable to have access to the private papers of people like my great grandfather. It provides a real connection to a man, time, and place which I couldn't know in person.
Perhaps publishing everything is a step too far, but things like semi-private diaries from a war or a voyage --- intended for immediate family to read, but not for publication --- are often okay to publish within living memory of the deceased. Sufficiently chaste love letters seem to me to be okay after a long enough time has elapsed, too.
Maybe the living will care, but maybe we should not care that they care.
After he died, the entire erotic oevre of the artist William Turner was destroyed by his family on grounds of taste. If they were half as profound and amazing as his landscapes, then this was an act of profound desacration.
If that is what you wish, then absolutely, publish everything. Where I question the morality is in private correspondence, a persons dairy and things which was explicitly never wanted to be published.
There are movies, music and books which the creators specifically withheld from the world. Who are we to determine otherwise. Again I see no issue in researchers combing over half-written books, discarded sheet music or personal notes. I just think we should be respectful and keep things that was deliberately hidden from the world private. If an author leaves a 90% finished book and say they don't want it published, having family or publishers to going ahead, finishing it or publishing it in its half-finished state anyway after the death or the author doesn't sit right with me.
That's not to say that something like Feynman letter to his wife isn't beautiful, it is, very much so. It was just not meant for us, it was meant for himself and a woman who would never read it.
After I am dead, publish everything, correspondence, search history, location history, nude photos. I am dead, I cannot care.