Even YouTube must continue to support Flash video for at least another year because many websites embedded Flash videos using YouTube's boilerplate embedding HTML with the Flash <object> tag. Google can't magically rewrite these third-party websites' HTML. :) Maybe YouTube can use some SWF that loads or redirects people to youtube.com? Or browsers could recognize YouTube's boilerplate embedding HTML and rewrite it with YouTube's HTML5 video.
Flash, while pretty atrocious, is part of the cultural legacy of the web.
Someday shumway may be the only way reasonable way to access this via archive.org etc.
Note that for a lot of content, it's not even required to use Shumway in the form of a browser extension or built-in system: it's perfectly possible to run SWFs with Shumway as a website-deployed player. E.g., the header on http://areweflashyet.com is deployed that way and works just fine in all modern browsers.
Browsers themselves don't need to do it. It could be a (very useful) browser extension or a user script.