Mouseovers were just the tip of the iceberg: fixed screen sizes and other desktop UI conventions, assumptions that you could just leave things constantly running rather than figure out how to do proper event-driven programming, etc. Yes, they could have tried to do a “Flash mobile” but most of the appeal was compatibility with the huge library of existing apps and users wouldn’t have been happy with that, while authors would have bristled at having to give up their favorite hacks. Flash was a fractal of bad programming and UI design, and there was no way to get that community to improve since Adobe was one of the worst offenders and didn’t care about their platform in any discernible way. People wrote Click-to-Flash plugins to keep it from crashing your browser, every browser had to change their architecture to handle Flash crashing, the plugin & authoring tools had tons of performance, stability, and security issues – and Adobe just kept snoozing, waking only enough to cash the royalty checks, and claim the next version would be totally better.
Another poster mentioned the hangs - which is very true - and I can say that the desktop Macs I supported had a high 90% of the crash logs show Flash as the culprit, not to mention almost every CPU / battery life issue.
There were some great artists who produced neat work despite it but the only company to blame for Flash’s demise is Adobe. As a thought exercise, ask why Flash on Android consistently sucked – if they were trying to make the case that Apple should reconsider, they could have put at least one intern on making that seem appealing.