Maybe, portability (don't have to build three binaries) and security (VM sandboxing)?
However, the performance hit (I'm using emscripten/asmjs) isn't negligible (and the browser introduces some lag), which means there's no way I'm dropping native build support for my games.
It could be a new business model: play the web version immediately for free, buy the native version if you want speed/smoothness.
This is also why people tend to use a framework like Unity, or a language like Haxe both of which allow you to write once, compile lots of places. I don't have much personal experience with either, but Haxe pops up in a lot of threads where indie developers hangout, and even AAA game devs seem to use Unity.
I suspect it's sort of the same problem that Java has, where it's write once, debug everywhere, but there are people who swear by them, and I suspect that once you get some experience you tend to avoid writing code that causes cross platform debugging headaches in the first place.
My sense is: not easy. WebGL is fantastic, JavaScript can perform great it you are smart about it, and you can compile anything to ASM.... But none of those techniques are automatically a good fit for a game architecture designed on Windows or Playstation. For things to work well, you have to design for the web technologies from the start, everything from gameplay to assets has to take into account the limits of the web platform.
But, if you do it right, the web is the only place where you can get things like instant boot, continuous deployment, and lots of other goodies.