I'm having a look at the Rebinding scene, and it looks like rebinding makes heavy use of PlayerPrefs internally.
As you probably know - PlayerPrefs isn't supported universally on all platforms, especially on console (even though they kind of work on a surface level). This kind of limits the platforms Sinput can be used if I want to make use of the rebinding system.
I was thinking instead of saving the Rebinded keys to PlayerPrefs, couldn't you just create a new control scheme with the rebinded keys? The game just needs to remember that the player's using a custom scheme. When the player clicks 'reset to default', the custom scheme can be deleted and the game can go back to using the default scheme.