Good question - I have no idea who Silverlight is for. It might make sense for internal corporate applications - but they don't need to look very pretty so all the integration with design stuff is irrelevant.
But that's more a testament to the vendor's "now with $AWESOME_PLATFORM!"-driven software architecture paradigm than any real fault of Silverlight or Java. (Except that they both appeal to those sorts of people.)
You see it a lot in the enterprise world.
Facebook also has a couple of applets I think.