On the other hand, something like https://github.com/brion/ogv.js/ is actually doing all of the decoding and playback in JavaScript/asm.js, using C libraries compiled with Emscripten.
Anyhow, yes, it probably would be possible to package up extensions that would apply one of these automatically to <video> tags with unsupported codecs or container formats. It's just a simple matter of programming.
[0] https://github.com/dailymotion/hls.js
[1] http://open.blogs.nytimes.com/2016/02/08/flash-free-video-in...
However, isn't this server side and not clientside?
Here is an example of playing HEVC with this method: https://strukturag.github.io/libde265.js/