I mean that's still basically what they tried to do at the time. They were trying to get them through web standards committees and everything.
IIRC a big reason it didn't end up working was because NaCl was such a "big" technology and asm.js such a "small" one that asm.js was able to reach production-ready first despite starting work several years later.
The big difference was that they lacked the market share they enjoy nowadays, with their forks and Electron crap.
The cute thing about asm.js is that it was fully backwards compatible with the web: it was just a lot slower without dedicated support. So Epic or whomever could put out a demo that would run just fine in Chrome, but the performance was a lot worse than Firefox which had a dedicated compilation pipeline, so it made Chrome look bad.
Exactly. "You can't not support it; you can only be slow."