When I die I hope people don't decide to begin sharing my private conversations.

When you die, there will be nobody to care about that

I’m sorry to inform you, but that’s often how we preserve history...

E.g. http://www.nationalarchives.gov.uk/education/resources/lette...

Should we destroy these letters too?

Oof, I'm guessing you're not a big fan of biographies or history books.