All of the sites with Applets I go to do this in Chrome on OSX (unless I've explicitly said the site is trusted after the first time I run it) (Can't recall a site off the top of my head, else I'd post a screenshot)

It's probably a browser feature, not a Java feature. Firefox also does this.

That's the browser, not the plugin. We added it to Chrome a few years ago for out-of-date plugins, and plugins that have a bad track record on fixing their vulnerabilities (e.g. Java). Firefox recently added the same thing for out-of-date plugins, and just this week started doing it for all versions of Java.