I can echo your concerns because I ran into it with Spelunky recently - they seem to only support Xbox360 controllers as their "controller" settings. I solved it by using Joy2Key to map keys to my controller (a very solid Logitech one!) and had no problems.
However, most people probably wouldn't want to jump through those kind of hoops (downloading a third party app + mapping the keys to the right keyboard keys) so I'd love if Steam had some sort of unified controller support, but I also feel like that's asking for a lot.
This is a pretty recent change in how controller support works in (Windows? DirectX? not 100% sure) but basically any third party controller can register itself as an Xbox controller.
I have an older Logitech DualAction and a newer one, the older one will fail those checks but the newer will register itself as an Xbox controller. It seems like Microsoft, somewhere, standardized what it means to be a "controller" finally instead of having an arbitrary button0 through button10 that are always different and constantly requiring remapping.
A good change, but really frustrating for anyone with older hardware.
However, most people probably wouldn't want to jump through those kind of hoops (downloading a third party app + mapping the keys to the right keyboard keys) so I'd love if Steam had some sort of unified controller support, but I also feel like that's asking for a lot.