Think of how many family recipes could be preserved. Think of the stories that you can be retold in 10 years. Think of the little things that you’d easily forget as time passes.
An AI isn't going to magically know these things, because these aren't AIs based on brain scans preserving the person's entire mind and memories. They can learn only the data they're told. And fortunately, there's a much cheaper way for someone to preserve family recipies and other memories that their loved ones would like to hold onto: they could write it down, or record a video. No AI needed.
I also suspect, based on the accuracy of AIs we have seen so far, that their interpretation of the deceased's personality would not be very accurate, and would likely hallucinate memories or facts about the person, or make them "say" things they never would have said when they were alive. At best it would be very Uncanny Valley, and at worst would be very, very upsetting for the bereaved person.