It seems to me that we should really be looking for browsers to compile (or at least appear to compile, even if they skip this as an optimization) Javascript into a lower-level 'assembly' language, so that Dart can be made to compile to the same form. A LLVM for browsers, basically.
JS is a terrible assembly language. But the work that's been done on making it passable for that purpose is remarkable, so we're getting by with it.
You have to ask yourself if it's easier to get all browser vendors to agree on an intermediate language or to get them to agree on new apis that makes javascript better for that purpose.
Is that one of those things that "nobody" willingly installs in their browser unless they absolutely have to because much of the market doesn't even understand what they are and the ones that do still want to avoid them because they decrease browser stability?
Quite literally; there is a section of the Mozilla browser codebase that actively seeks out those plugins (along with QuickTime, Windows Media Player, and Acrobat Reader) because users who lack them experience a "broken web" (http://lxr.mozilla.org/mozilla-central/source/dom/plugins/ba...).
I'm not saying becoming one of those plugins is impossible---clearly, it's been done more than zero times. I'm saying that I really wouldn't base any business decisions around the assumption that it will happen for your plugin.
People adopt new things all the time. Look at what happened when smart phones came long - everybody started making apps for them. I think people on smart phones spend more time in apps than they do on the web.
Anyway, the new browser could totally embed another browser engine to show legacy web pages.
New browser that fully supports existing technologies is probably the best option.
Similarly, there's nothing technically stopping someone from building a new scripting core in the browser itself and then implementing the JavaScript engine atop that (other than the need to support a brand-new untested framework in an environment of high-performance already-existing JavaScript engines, of course).
JS is a terrible assembly language. But the work that's been done on making it passable for that purpose is remarkable, so we're getting by with it.