A single physical USB device can enumerate as multiple virtual devices. This lets you easily side-step the limits *if* the game supports input from multiple controllers at the same time. The games I use controllers for allow you to map to multiple controllers, mouse, and keyboard, all at once. The touchpad could simply enumerate as a HID Touchpad. Apparently Windows already has a Touchpad Haptic HID Profile even.
Honestly, if Valve is making you require Steam to fully use the Steam Controller, that's disappointing because, as far as I can tell, nothing it's doing can't be accessed via HID usage.
Microsoft has a new API with GameInput that addresses this situation and allows mapping Generic HID devices onto game controller via config file, but it doesn't work retroactively, it only works for games that use the new GameInput API.
Valve could of course provide a way to switch and emulate other protocols too, just like other third party vendors do, but there is no USB standard that makes things "just work" in Windows when it comes to gamepads, you always need extra drivers, USB modes or other hacks.
On consoles the situation is even worse, modern consoles deliberately lock out any unlicensed third party controller. Playstation3 was the first and last console that supported standard USB controller, while PS5 doesn't even support PS4 controller.
But it's all a bit theoretical, since most modern gamepads have Xinput support, and the generic HID devices are mostly flightsticks or SNES-style gamepads that wouldn't have enough buttons and axis for modern games in the first place. Another issue is that most games don't offer input remapping for gamepads.
But with SteamInput and homebrew tools like x360ce there are many ways to make generic USB devices compatible Xinput, so it's not like you can't use them. It's just not something that works out of the box.