Thing is, in the games I run/play in each player has numerous characters in the setting; and a story consequence that matters deeply to one character might not affect another of the same player's characters in the slightest. As such, the players (including me) tend to distance ourselves a bit from story consequences unless we're playing a characterat the time who is directly affected.
ALL characters, however, are affected by big-time mechanical consequences such as level loss, item loss and death; which means the player will also be affected no matter what.