Not all of Java is open source. The TCK, the testing suite for standard compliance, for instance, is proprietary, and only organizations with Oracle's blessing can gain access. AdoptOpenJDK was only granted access after they stopped distributing another Java runtime, OpenJ9.
The only advantage to Java applets I can think of is that they had the advantage of freezing the browser so it could no longer be hacked.
The Java applet system was designed better than ActiveX but in practice I've always found it to be so much worse of an end user experience. This probably had to do with the fact most ActiveX components were rather small integrations rather than (badly fitted) full-page UIs.
One exception is early 2000s Runescape: that was Java in browser but always loaded, no gray screen and hanging browser. They knew what they were doing.
It's not a perfect fit, but it works. The speed of Ruffle loading on a page is similar to that of Flash initializing, so you can arguably still make flash websites and animations to get the old look and feel if you stick to the Ruffle compatibility range. The half-to-one-second page freeze that was the norm now feels wrong, though, so maybe it's not the best idea to put Flash components everywhere like we used to do.
Runescape proved that Java could be a pretty decent system, but so many inexperienced/bad Java developers killed the ecosystem. The same is true on the backend, where Java still suffers from the reputation the Java 7 monolithic mega projects left behind.
Can a person not run Flash authoring tools with an era-appropriate operating system in a VM or something?
Macromedia also provided direction, focus, and marketing; more of the things that allowed Flash to reach saturation.
Someone could certainly come up with an open JS stack that accomplishes some of the same things in a browser on a modern pocket supercomputer. And countless people certainly have.
But without forces like marketing to drive cohesion, simplicity, and adoption then none of them can reach similar saturation.