This is what Android does with Dalvik/Android Runtime. Apps you download from the store are compiled to bytecode that is then compiled to native code at installation time.

With the compilation making use of the native instruction set supported for your device, so it can make use of newer arm instructions on newer devices while still supporting older devices.

This is the major reason app installation is so slow in Android compared to iOS (which pre-compiles everything). But it also greatly improves app compatibility with older versions.

There is no way Valve would be able to convince all the myriad of game engine developers to support a proprietary (or even open source) bytecode format even in the future. Best they could do is make it an opt-in.

Android only pulled it off because Google provides the "engine" (Android SDK) for all apps made for the platform and it did from the start.

And even so, most Androids games actually bypass this system entirely and just hand-compile to native binaries anyway. Because, again, the game engines don't want to support this bytecode format and google doesn't offer a C++ toolchain themselves that the engine developers could integrate with.