Imagine all of the 1-2 decade old applets that no one will care enough about to update. I'm thinking of little physics simulators you'd find on a professor's web page to simulate projectile motion and such.
On the other hand, the Java bytecode is simple enough that it shouldn't be too much work to write an emulator in JS, and, as most of Java is written in Java, all one really needs to write around that is a shell for the AWT and maybe a bit of class/string functionality to get the viewer working. Threading and I/O would be a truly nasty pain, but you could probably bypass most of that.
I'd be more surprised if there weren't already some attempts to work on this.