The point of games is that the journey is more important than the destination or conclusion, so really it doesn't matter all that much if you stick to the save-game conventions or not. Problem is that any save-game related choice in design should never interfere with the fun of playing the game. The problem of not going by the save game conventions is that a.) you might confuse gamers and b.) the alternative solution should still punish or reward players for failing the initial level. If you choose not to punish players, then the alternative 'reward' should make sense and be something that can be done over and over again as people theoretically could fail a mission dozens and dozens of times. The latter choice will most likely end up with design solutions like in Bioshock.

Examples of bad save-game designs would be Soldier of Fortune-Payback, but also for example Bioshock. In Bioshock dying doesn't punish players because Big Daddies for example get to keep their health at the level you'd damaged them to before. You can kill a Big Daddy with a wrench if you'd wanted and don't care to respawn a couple of dozen times. Somehow.. the save game mechanic in that game felt kind of broken.
In Soldier of Fortune Payback you'll be begging for more save game checkpoint spots, because of the difficulty of the game. It's one of those games that theoretically only takes you roughly 6 hours to finish, but you will play at least double that time because of the countless retries you will be doing. They should have added more save-game checkpoints,

Cheers