Likely because Netflix relied on Silverlight for video playback early on. I'd be surprised if they still had C# in their front-end stack (and I say that as a general C# fan, though I use it on the back-end).
My favorite thing about it having Silverlight is Silverlight actually worked on Linux better than Flash did. I think I used the Mono version of it though, I don't remember?
I remain of the opinion that there was nothing wrong with Flash or Silverlight, and the only reason it fell out of fashion was that Apple refused to support it on iOS.
Don't care about losing Java applets though, those things were too heavyweight for what they did. And more advanced stuff like Windows Update running through a browser was major security incidents waiting to happen.
