While I do understand where you are coming from - it can be more convenient to target a single implementation - the fact is that Flash has not been what you describe, for a while now. Flash officially announced it would no longer support Linux, and Flash is not usable in most mobile browsers either, for example.
Even plugins can't really get you what you want here. Yes, HTML5 has limitations, as you described, but plugins aren't the solution. HTML5 is closer, and moving in the right direction at least.
Mobile doesn't need browser plugins, because it has apps. AS3 compiles to Android and iOS, just as it should. So I agree with Adobe that mobile doesn't need to support Flash. BTW, the same AS3 codebase for Flash runs as mobile apps. Do the HTML5 games support all versions of all browsers on the most popular mobile devices? Not on mine at least :(.
One codebase, runs everywhere, Flash in the browser, apps on mobile devices. Personally never had an issue with it.
Although I must agree with you that it's sad Adobe dropped Linux support.
koonsolo is right on with all his points. Flash is better then HTML5 all around.
Though personally I can understand why Adobe dropped support for linux, the market is just too small. Even though this community probably has a higher percentage of linux user then just about anywhere.
Yeah and this community is made up by mostly developers. To turn your back on developers is shooting yourself in your own foot. However, that is not what adobe are doing. They have signalled their intention to sunset flash themselves for a long time.
Plugins allow you to more easily experiment with different distribution methods, languages, etc. Flash, Unity, the JVM, etc, all have areas that they're much better at, such as tooling support, language support, etc. Sticking everything in a monoculture is a terrible idea.
Even plugins can't really get you what you want here. Yes, HTML5 has limitations, as you described, but plugins aren't the solution. HTML5 is closer, and moving in the right direction at least.