To say that asm.js and WebGL are "narrow in focus" is like saying x86 is "narrow in focus". They're general-purpose primitives that can be used for a wide variety of purposes. UDK, Unity, Gamemaker, Construct all export to HTML5. Flash has achieved a huge degree of success, so if it goes away maybe the next contender will be less damaging, but the mistake can be remade at any point, and with the power of asm.js/WebGL almost any framework can be ported.
People have always abandoned the pure, semantic HTML way as soon as the power has been there to do so. Sometimes this has been for good, sometimes for evil. You need to either turn it into a general purpose computing platform (Mozilla have been fighting this for a long time and finally lost) or leave it as a pure document browser (in other words, an application rather than a platform). But since people always want cooler, shinier things delivered faster, and the web provides fast, sort-of-safe delivery, there will be pressure from many places to start trying to eat up some of the native pie, which is how we got here in the first place.
The web people got everything wrong. They pushed a ton of waffly high-level rubbish trying to hang onto a restricted, comprehensible model, but in the end they had to cave and stick all the powerful stuff in anyway, and on a C-machine that means something like C (hence asm.js, which is a C compile target). And what we've ended up with is, frankly, pretty shit. The whole idea of nice, semantic HTML only works as a restricted application with no client-side programming facilities. Maybe in 30 years someone will have the sense to lift it out into the "user land" of the browser where it belongs.