Although I don't have numbers, I'm not aware of very many enterprises with extensive fleets of java applets. Java in the enterprise tends to be either stand alone programs (i.e. Swing), or EJB driven middleware with JSP on the front end.
Most of the apps are little more than forms - there's a lot of logic in the way the different fields are filled out and the validation and business logic is probably quite complex. Since everything must be checked on the server anyway there's nothing stopping it from being migrated to pure HTML.
Is there a reason that Sungard HE can't handle the browser portion using JS or similar instead of JPI? No. But it would be a very slow migration process and, basically, all employees at many major universities would be stuck with older Java versions.
This is just one example that I'm (unfortunately) intimately familiar with. I'm sure there are many others that the typical HN crowd (small shops, latest technology, devops, etc) would never see.