We cannot easily write applets down as there are way too many good code on a web. Lots of it was written by people who are not specialists in software development but are specialists in various high end areas that they tried to explain and illustrate with the help of Java applets, the top technology at that time. They may not have time to learn new language and rewrite they work any. Many are not active for years.
I also see Java applets as more appropriate for community projects that are based on server side builds and code reviewing. Various fancy user friendly tools can make development of web components fast and easy but the result is either not human readable at all or very difficult to review.
We have recently launched the Ultrastudio.org project that still relies on Java applet technology. I was thinking a lot about putting more languages and platforms but at the end was forced to conclude that it is either less secure or otherwise way more complex to do.