Until you run into one of the things that Java doesn't handle by itself, such as gamepad input, OpenGL graphics, webcam access, etc. Then you have to install native code. Or until you run into a platform that doesn't have a JVM. I know of plenty of platforms with a web browser but no JVM, and I can list them if you wish.
not having to beg each platform's owner (like Apple, Microsoft, Nintendo, or Sony) for permission to run your application
I'm not talking locked down environments here; I'm talking environments in which you'd actually play a game or use multimedia software, i.e. at home/on your own computer.
A lot of people prefer to "actually play a game" on their own game console at home, and game consoles other than OUYA are locked down environments. They don't run Java applets or Java applications.