There's another huge problem with writing a browser in Java (or any other JVM-based language), which is that your browser would be dependent on the user installing the JVM, which is a separate product from a separate company that has a separate release cycle (and lots of security updates to deal with). It's hard enough to support a browser like Firefox or Chrome without dealing with issues like the user having Java 1.5 installed but the current version of the browser requires Java 1.6 or above. For a non-technical user who barely knows the difference between their browser and their operating system, there are huge obstacles in supporting software built on top of the JVM.
I feel that additionally there is some user resistance to installing and using the JVM. It may be minor, but I do know some people that won't touch eclipse with a 10 foot pole due to that.
