I understand that saving works well in some games, like Jump King for example. I am just saying I don't think it would be good for Teleport Tower because of its specific mechanics.
Adding on to this, here are the reasons I think this shouldn't be made a strict requirement:
1. It is a high bar for new game-devs. For Jump-King it might be easy (just player position + velocity), but for games with more than just player-state to save, it is non-trivial. Dealing with save-file versioning also adds extra complexity.
2. Saving must be continuous (at least once a second) to avoid it being exploitable (alt-F4 when you fall). For games with a lot of state to save, this may not even be possible due to the lag it would introduce.
3. Foddian games make it both harder to patch in (no existing checkpoint system), and less necessary (not being able to save is the point). Some of the submitted games simply will not need it.