My first response is that writing in ancient times, even letters, was always intended for an audience of more than a few people. The only writing I can think of that approaches journal writing with references to private topics: moods, culpability, remorse, self-questioning, trivia of daily life, is the Confessions of St. Augustine, on the eve of the medieval period. I'm sure others will have sources for you.
"Dear Diary,
It's nine o'clock, the children are fast asleep, and I'm going over these latest accounts from Trajan's Market before I hit the sack." Ancient people didn't conceive of their world or of themselves in this way.
True, plus in ancient times the writing materials were expensive so it isn't likely to be wasted on writing a diary.