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.
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too far, but things like semi-private diaries from a war or a voyage --- intended for immediate family to read, but not for publication --- are often okay to publish within living memory of the deceased.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.
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.