At some point the browser vendors started addressing that, and things got better.
But I think the other part of Flash is the tools used to create it - I never understood why they didn't port those to HTML5 and worked with the browser vendors to get kinks ironed out, instead of doubling down on - what was the name - Adobe Air? I think they still had some market power they could have wielded.
In late 2000s they owned the Web App space ( what was called Rich Internet Applications in their speak). Flex (their business GUI components library and markup language) was absolutely dominating corporate Web app development.
And they just abandoned it.
In an alternative reality we are all building HTML5 Web apps with Flex Builder right now.
The Flash Player is, at the end of the day, a proprietary Canvas widget with a ECMAScript based VM powering it. With HTML5 they could have targetted the actual real HTML5 Canvas and completely eliminated the flash player plug in whilst still retaining the tools.