If you want IDE features, use an IDE. Using Java as an example, if you are a Java developer, you should be using Eclipse, or similar. Yes Eclipse is heavyweight, but it is so for a reason. Eclipse has millions of lines of code, with hundreds of developers, working for many years. To think that Sublime could even approach this level of sophistication is completely unrealistic, even if we wanted it to be so. But we don't. We want Sublime to be a lightening fast text editor; that is all.
If you think that Eclipse, etc. are simply glorified text editors, then you probably aren't utilising your IDE to its full potential. Likewise if you think that with a few plugins, Sublime would make programming in Java so much better.
The example of showing Javadocs is a perfect. There is a lot of code and configuration that goes into that view. First it has to know what the classpath is for the given project, then it has to know how to resolve this classpath, then it has to parse the Java source, then it has parse the javadocs, then it has to render it in some html hybrid kind of view, then it has to provide a browser like UI to allow navigation. Then it has to do this continuously in the background to keep it in synch with recently edited code, or recently modified classpath. In short, Sublime can not do it, and its unfair to ask.
There is of course always scope for plugins to add useful features here and there, and for many scripting languages that don't really require fully fledged IDEs, e.g. Python, this might be enough. (Although since I started using an IDE for Python, I wouldn't go back to using just a text editor for that either).