Java failed to be what JavaScript became for a number of reasons, but I think the primary was the fact that it never integrated with HTML as cleanly as JS.
It could have been JS, but it was strangled to death by Sun (on the client).
Java also has the problem of long startup times while the JIT is doing its thing. Javascript has always just started executing right away. Waiting a minute or two for a Java loading bar wasn't fun.
JavaScript hasn't always worked that way. My guess is that if Java had become the tool for this, then it's startup times would have been fixed. Pure speculation of course.
It could have been JS, but it was strangled to death by Sun (on the client).