I see. I'll try to avoid those pitfalls when designing the rebind menus in my own games in the future. Thank you for sharing your unique viewpoint.
Out of curiosity, doesn't Steam offer something similar with the Steam Controller Input menu thing? The one that lets you configure and rebind your controller on a per-game basis, and even emulate KB and mouse with it. I think you can add non-steam games there and still use it if I'm not mistaken. How does it compare to JoyToKey? Note that I haven't used either of those.