This feels like such an odd requirement for this genre specifically. For my game personally I feel like a save feature would only add confusion and detract from what the game is. Are there no exceptions?
I want refreshing the page to take players back to the very start of the game, before the intro cutscene. I do plan to add a reset button, but I want the reset button to take players to the beginning after the intro cutscene, as it would be annoying for speedrunners to have to watch the cutscene every time. Saving would prevent players from being able to rewatch the intro cutscene. Saving is also just not that useful in our game due to the nature of the 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.