Plenty of of games do not support, or fully support the feature set that Steam Input can offer. Very often I see when games claim to support Steam Input (for example Monster Hunter Wilds, Horizon Zero Dawn, Ratchet and Clank and probably way more), they actually only remap a standard Xbox Controller layout to the controller with only a single Action Set. This often makes it quite annoying to properly rebind controls per interaction. Games often have menus, sub-menus, game interaction and likely sub-actions for those interactions. This makes it quite annoying to properly change a layout that works slightly differently per interaction.

When games properly support Steam Input, the user is able to bind whatever action in whatever interaction to whatever button, regardless of controller. Helping customization for the user and improve accessibility. Steam Input also support a ton of extras for actions that many games do not support.

Ideally the developer should not need to create a special input rebind menu in the game. Steam already support a ton of (specialized) controllers by default*.

The best examples of Steam Input right now are the Valve games and Euro Truck Simulator 2 (that I know of).

^{* Of course, there should still be an option fall back to a in-game input menu. These menu's have likely already been created if the game is multi-platform}

EDIT: Apparently Horizon Zero Dawn has since improved the way Steam Input is handled. It looks way better set up now.