But, you need people to download and install your app in that case. The reason major game companies are investing in asm.js ports, even though their engines work great natively, is because the web is a very good distribution platform. That's really all there is to it - no one controls the web, there's no charge to ship a game there.
I also think pouring millions of man hours into a transpiler and JavaScript engine optimizations is probably the least efficient and most convoluted way to take advantage of the web as a distribution platform. I think the way this should all be framed is, "it would be better if browsers supported a lower-level bytecode, or more languages, or both, but that's politically impossible to achieve, so we have asm.js". That's the only thing that makes sense to me here.
Perhaps Microsoft will tier their products in a different way. A Office 360 subscription (or whatever it is branded) will get you access to Office, running in a browser, under asm.js. Perhaps they'll do something different. Sooner or layer, however, the Microsoft embrace of this technology will be monetized.
There are side-effects. Microsoft can sell tools that now run a tranpiler to put executables on the web. They might or might not use LLVM to that end.
This development means that asm.js has become a defacto standard. It is too soon to tell if this will be more widely adopted, as defacto standards fail al the time. I think, however, that this one will stand. Quite likely we all are now going to be freed and constrained by small design decisions made long before this adoption came to pass.