I'm not sure I experienced the game as intended as I started the story mode, then basically thought "ok, this is a tutorial and probably adds some flavor texts". After the story mode was finished I played the regular game, but at that point I have seen most upgrades and depths. So basically, as far as I can tell the story mode doesn't add much to the player experience (in terms of story / lore / drama), but it does spoil the game quite a lot due to very quick progression.
I guess a warning to not start with that mode would be good for new players.