What you're missing is that there is no need to do that. Using JavaScript as an intermediary representation for other languages on a permanent basis is kind of ridiculous. Improving browser support for JavaScript-as-IR provides no benefit over adding support for a "real" IR and introduces superfluous complexity which is the enemy of both performance and security.
Compiling other languages to JavaScript is a tolerable transition mechanism while browsers that don't support something better are still popular, but trying to improve the ability of browsers to interpret compiled-to-JavaScript code from other languages is farcical -- if you're going to update the browser then update it to support something better than JavaScript, not to improve the performance of the horrible legacy transition kludge.
I don't disagree with anything you wrote, except the first sentence.
But I'm cynical about the possibility to get a new bytecode standard out, without e.g. MS sabotag... extending it. Half the value of asm.js should be that if there is a working system already in place, the motivations for such shenanigans lessens.
EEE wouldn't work here. That only works when you have overwhelming market share. Microsoft has basically no browser market share on mobile and even on the desktop they no longer have so much that developers can afford to ignore everything else.
The way to handle Microsoft in a situation like this is to ignore them. Support the same IR on Firefox, Chrome and Safari and then Microsoft can play along or go home. At that point the worst they could do is implement an extended version that allows sites made for all browsers to work with IE but then encourage developers to make sites using Windows-specific features that won't work on other platforms. That's effectively what they tried with Silverlight and you see how far that got them.
Compiling other languages to JavaScript is a tolerable transition mechanism while browsers that don't support something better are still popular, but trying to improve the ability of browsers to interpret compiled-to-JavaScript code from other languages is farcical -- if you're going to update the browser then update it to support something better than JavaScript, not to improve the performance of the horrible legacy transition kludge.