Java Applets had fallen out of fashion long before then. Like a decade earlier. The only reason browsers and JRE continued to support it was because of enterprise middleware like Oracle. But for home users applets had long since been replaced by Flash.
The reason applets were unfashionable had nothing to do with control. It was because:
1. They were hard to support: there was different Java runtimes (thanks to Microsoft creating an incompatible version of Java, which eventually lead to them inventing .NET). But even with Sun Java, there are different versions of JRE and no way to guarantee a particular browser had the right version of JRE installed.
2. Insecure. I really don’t miss the days of drive by download exploits
3. Too much effort to program for. When you had Flash with its mostly drag and drop interface, why would most people want to learn Java?
4. HTML5 eventually became a thing. Meaning you didn’t even need Flash let alone Java.
5. Applets were never ported to mobile devices. Which is ironic given Java runs on a plethora of niche hardware from some types of optical storage through to Android itself. However applets themselves were strictly limited to desktop browsers. A limitation even Flash didn’t have.
Java applets were removed because it was a technological dead end. Users hated it, security teams hated it, Windows administrators hated it, and web developers didn’t even use it.
I can’t remember exactly when I fell out of love with applets but I have a feeling it was before even the 00s.
And as for your point about control, you could still do everything you described without the need for applets. It was really easy to rip streams back then (just as it still is easy now).
