I also thought about solutions like this for a while, but frankly, every option sounds like the attempt to fix a leaking dam using duct tape.
Things like this have to be implemented properly. The problem is that this ties into the core architecture of the platform, not only the language - references are basically the most important implicit primitive there is in the CLR (implicit because not even the IL handles them like the other datatypes).
I'm not very informed on the subject, but I suspect that without a proper way to declare locals and members non-nullable in the CLR, the matter would get rather complicated - there'd be no possibility to communicate the requirement through method signatures, for example. And since you could call pretty much any C# method from other languages, I'd expect various problems there.
Of course, one option would be to only handle the initialization and assignment checks in the C# compiler (I guess that would be much easier) and simply generate conditional ArgumentNullExceptions in every method, but I suspect that this would be a problem for performance reasons.