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).
