The nice thing though is that, although the added attack surface is there, its not really accessible to web pages until a user grants the necessary permissions. Not really all that different from telling users to execute a native app in that respect.

In this case it's not even an exploit really; more like social engineering. (Tricking users into granting the phishing site unrestricted access to their Yubikey, then using that access to trick the user into authenticating a login session for the phishing site.)