.Net Core has API's that aren't applicable to the Windows full-fat Framework, Mono or Xamarin - you don't need or want them there.
For newer .NET implementations we push folks to start with .NET Core and adding their specific technologies on top. That is, for instance, what Samsung has been doing with Tizen. So if the open source community innovates in .NET Core, Samsung can just move to a later build of .NET Core in order to benefit from it. They are a pure superset of .NET Core, by construction. However, for all other cases someone needs to port the changes from .NET Core to Mono which makes it consumable by Xamarin and Unity. .NET Framework is in a similar boat, although porting is somewhat easier as the .NET Core code base originated from .NET Framework.
Since we can't (easily) move Mono/Xamarin/Unity/.NET Framework on top of .NET Core, we need a way to standardize the API set so that it's not all chaos. And that's where .NET Standard comes in.
The whole thing reminds me a little of the UI situation. Start with Winforms, don't improve it but start WPF (and keep Winforms), then start Silverlight, then start UWP. All in parallel instead of building on top of each other.
MS doesn't need more more frameworks, but less.