The problem with this approach is that as soon as you need to call out to a library written in a different language, it has no understanding of your lightweight green threads - precisely because it is currently a language/VM abstraction, not an OS abstraction, so everyone rolls their own. Furthermore, existing languages (notably, C) produce a legacy burden that'll remain even once OSes do start to add such threads.

For what it's worth, Win32 has offered a kind of green thread (fibers) for a very long time. Adoption has been minimal, even for other Microsoft products (e.g. .NET doesn't really support them properly).