With U2F, however, a per-host keypair is generated during the setup process and the public key is given to the remote server. Critically, the hostname as seen by your browser is part of the key identifier: see http://security.stackexchange.com/a/71704/311
That means that if in the future even if someone convinces you to visit their phishing site and activate the token, the login attempt will still fail because the hostname as seen by the browser won't match a key on the token.