Why can't static method in non-static class be an extension method?

At compile time whenever you use the instance syntax sugar for extension methods, this is converted into a call to the static method (which defines the extension), and passes through your instance.

Apart from the nice syntax it's no different to implementing a static method and passing your instance through as an argument. This is exactly what happens. You can't do this with static classes, as you can't pass a static class as a parameter to a method.