The original use-case would have been something like: imagine you code a game physics engine in Java, and deploy it as a Java applet. You can embed that physics engine into a page as an <object> — and then consume it as a local API using JavaScript embedded on the same page.

(And yes, this is almost certainly the real reason JavaScript is called "JavaScript." When it was created, it was precisely positioned as a glue language for consuming/driving Java-applet APIs!)

Java-applet-based APIs (and their Windows-proprietary ActiveX cousins) are dead, so there's no real reason to care about <object> any more. As long as the browser knows how to render the media if you navigate directly to its URL, you can just use an <iframe>.

It's not needed anymore for audio or video — they have their own tags now — and plugins are dead.