There are already some great answers here - but I think the question is not exactly right.
There's a difference between a hardware platform and the OS that rests upon it.
Imagine a free, universally available, top notch OS that works on all hardware platforms. Okay - not all platforms. There's a (ever-reducing) point where an OS is more than is necessary - such as the code required to drive an electric toothbrush. However, as we continue to develop hardware implementations, it is becoming increasingly cheaper just to use the same codebase for everything - so yes, at some point even a toothbrush could be available as a hardware platform.
Once you have a good OS that runs on all hardware platforms - the requisite toolchain is available to run all software on all platforms.
Well... or fail gracefully (playing Doom on my toothbrush may be different unless it has a built-in screen and more than one button!)
A universal non-proprietary OS won't be (and cannot be) owned or commercially sold.
It's probably going to be Linux; Linux is about as close as you can get right now, and it conforms to Linux's own motives.
Timeline? I reckon that Linux needs another twenty years before Apple, Microsoft and other outliers throw in the towel.