Since 2004, Mozilla has had baked-in support for automatically installing Flash on the first encounter if the plugin is not found. A nice little yellow infobar pops down (a brilliant UI innovation), prompting you to install it with a few clicks, even without root access on both Windows and Linux.
They've also recently implemented automatic update checking for Flash. Since it's their biggest security hole, they throw up a big nasty "update now" warning on launch if you're using a known-vulnerable version. Mozilla even initially distributed the Flash binaries under license themselves via addons.mozilla.org -- I'm not sure if they still do so.
Flash is shitty, nonredistributable, closed-source, restricted-platform, proprietary, and patent-encumbered but they're willing to go to great lengths to help their users use it. Why not do the same thing for ffmpeg, which is merely patent-encumbered?