I doubt we'll see a letter from Tim Cook on the topic, but Java will probably be the next browser extension technology to be killed off after Flash and Silverlight. Of course, these deprecations are only on mobile to date, but smartphones and tablets likely constitute a majority of computing devices sold today. If your platform isn't on mobile, you are a niche player.
iOS seems to do an excellent job demonstrating that these vestigial technologies are no longer necessary in modern browsers. At this point, for most people, all Java provides is a less secure, less performant browsing experience.