Fear is DEFINITELY social... the reason WCVamps get to do mental is because they're actually nibbling on the target's psyche/chi through the emotion as a conduit. The emotion doesn't cause the damage, the WCVamp feeding does.
Even when they're using Incite Emotion's upgraded version (which does do Mental), they're going about it differently than your dragon, or clint eastwood... they're still digging around in the target's psyche to create serious lasting emotional states.
Intimidate is a social skill, so it should primarily do (90% of the time or more) social damage.
In rare cases, you can use Fists or Weaponry to deal social (Disgracing the target rather than defeating them) but it takes specific storytelling to manage. 90% of the time or more, they deal physical stress because they're physical skills.
Intimidate and Deceit and other social skills can, similarly, once in a while lead to mental or physical stress, but it should be WAY rare, and require either a power or specific storytelling (or both) to manage... like others have said, repeated incidents that it leaves a lasting mental disorder, as can extremes or powers... the rest of the time, I think of emotional states as social (they certainly have the bulk of their effects and related compels in the arena of the social), and mental is reserved for mental disorders.
RAW backs me up here... read YS216, it specifically mentions Intimidation as the core trait for SOCIAL attacks. It further lists several Social Consequences that sound a LOT like emotional states (specifically Stressed Out, Crappy Mood, Nervous, Edgy, and Guilt-Ridden).
As other have said, the section on mental conflicts immediately after stresses that it should be very very rare to do direct mental stress to a target without special circumstances (like a relationship with the target that lets you hone in on their deepest nightmares) or stunts/powers.
Also remember- what are you trying to accomplish? Recovery from any consequence requires an in-game justification. Are you trying to scare them off (so once they get away, and take a minute to breath, they can start recovering from any consequences), or leave them in need of a therapist? If you're genuinely convinced that what you're doing is capable of driving them to needing therapy... then mental is acceptable to me. Otherwise, just let it be social, and be done.
As for social defenses being rare... hardly. There are more social skills with built-in defense trappings than there are mental and physical combined. If you find social defenses are rare in your group, that's on your players and GM for choosing to completely ignore social defense.
