Forgive me if I'm dense, but I'm still not seeing what Firefox is doing wrong here. As far as I can tell, it's following the exact same method as everyone else -- it uses /etc/mime.types to map mime-types to file extensions, and it uses /etc/mailcap and ~/.mailcap to choose a default application. If you want to change the default application, then that's the only time you need to open up the file browser -- and I rarely use it to actually browse /usr/bin, I just type the desired executable name directly.
(Incidentally, the Freedesktop.org spec only seems to cover mime types, not mailcap. I don't see which of their specs covers default applications?)