browsers aren't well designed for truly interactive GUIs and aren't all that compatible from platform to platform either

On the contrary, there are a lot of developments that make browsers great for interactive GUIs. The problem is that most of them are specific to the browser (ActiveX, XUL, JavaScript, etc.)

Java is not the solution here. Applets are largely considered a failure (even though they were one of the orginal big reasons to use Java). Swing and AWT are too bloated and kludgy, even when compared to the rest of the Java API. Java found it's niche on the server side--exactly opposite from where Sun orginally wanted it in the 1.0 release. Oh, and cell phones, which are actually the sort of devices that Java was orginally targeted at back when it was called 'Oak'.