You say it is only possible 'in cut-scene heavy games', but is it?
It's very hard to do sadness in games cos it proper fucks up the reward mechanic. Well done on completing that level pepsipop. Your reward is... your mum dies. Congrats!
You can only really do it in cut-scene heavy games I reckon, where the cause of the tragedy is completely encapsulated in a cut-scene you don't control, so it's clearer that it's designed to happen like that, and didn't just happen cos you played badly.
Imagine for example a 2D platform game where the player gets involved with various tasks, and there's a second likeable/lovable character that's always there, and the player gets used to that other character always being around. Towards the end of the game, that character dies during a task, never to return, leaving the player to complete the game alone, with no partner, that could work on an emotional level. To reach the end alone (because that's the way the story is), when there should have been two, would generate a second sad moment.