I'd argue that at this stage, this should probably be the default. Further options to consider:

- Make it a singleton, or at least expose a static property with a single instance?
- Allow SetLogger(null) to use the NullLogger?

Coreclr doesn't support the StreamWriter(string) constructor.
Use File.CreateText() instead, which is equivalent and supported on all platforms.

Coreclr doesn't support Assembly.GetExecutingAssembly(),
use TypeInfo.Assembly instead, which is supported on all platforms.