Traditional death systems have a small number of checkpoints placed strategically around pockets of challenge, puzzle or heightened action, and the player will always travel back to this moment.
Giving the player a substantial amount of geography to traverse and challenge to overcome means that they must truly learn the game's systems, mechanics and in some cases, timing.
By sending the player back and forcing them to replay minutes of game play, it gives consequence to death, and forces the player to think about their actions and play better, improving their skill.
It also adds a massive level of satisfaction and reward when clearing a specifically tricky area, with a sense of relief and completion when the game notifies the player that they have met the next checkpoint.
Prince of Persia effectively adds thousands of checkpoints at every solid, level footed location, losing any real need to play carefully and resourcefully, and effectively negates any sense of satisfaction, challenge and, in more extreme cases, fun.