You don't always have that choice. There was a European country (I forget which one. Norway?) that was using applets for access to government services.
You can run Java selectively then, disable when not knowingly using it. Would provide a higher magnitude of security than just having it running while a rogue 0 day exploit hits advertisement servers or something similar.
Germany was it – until 2011 the only way to file taxes digitally was through a Java Applet called ELSTER. Now there is a beta version of a JS based solution.
Not to detract from your point, but the applet part of Norwegian BankID is now mostly replaced by the new Javascript-based solution.