At my house I have literally several boxes that they used to belong to my grandmother, before she passed away, and they contain an odd mix of junk and precious family history.
I am sure that this is not an uncommon story, and a lot of our history is composed of letters that were read after the sender / reciever were dead. A lot of the time this offers an unreplacable view of what really happened.
And if we try to look at less than the human history, then just having the possibility of going through the mail / documents of someone allows you to understand what is going on, and take actions with regards to it. (Such as paying the mortage)
I don't get any written letters anymore, excepts bills. Everything is done using emails. I am not unique. I keep a lot of what I do up in the cloud.
So, what happens when someone dies? To the best of my knowledge, there is no real process / precedant for that.
Even assuming that you have access to the passwords, would anyone would go through those emails in a hundred years? Would they be able to?