As far as I know, people like reading novels, so whatever you do, it cant be bad.
If its not conventional, at least your game will be more novel (hue hue).
So it just comes down to what is a better experience, and as you say, the plot would be better if you didnt force a particular way to show it.
(But do keep looking for existing examples for ideas on how to do it well)
Though make sure the gameplay doesnt motivate the player to ignore the text to find some single bit of information, or to skip it entirely. If the players own goals are to "beat the game", theyre not going to read through the story. So design it such that players are primarily interested in the story, or itll just get in the way.