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It's about databinding, let's say I have an object for binding to my UI and I want to hide show it based on other properties of the object. I could add an extension property for IsVisible or Visibility and bind that property to the UI.
You can't bind extension methods, but being able to add properties for databinding to existing types you can't extend could be very useful.
I guess it would be great, as long as there's no or minimal performance penalty in using them.