I mean, no phone controller has the same layout as the steam controller.

100% exactly the same layout is impossible, when there has to be room for the phone cradle in the middle. If you want to clip the phone above the Steam Controller, just get one of those plastic holders where you can attach the regular Steam Controller at the bottom side.

If Valve could implement the software to support steaminput when streaming games to a phone from your PC or a cloud PC, that’d be kinda cool.

Steam Link already exists and Steam Input runs on the PC.

a controller with feature parity with the Steam Controller would be an innovation.

The phone’s touch screen already provides the touch pad functionality when using one of the controllers pictured above.