I can't see a social master intimidating the heck out of a beast to be honest. Not without a lot of maneuvers to tag anyways. The fact is that social attacks in a physical conflict are always going to be less desirable to physical attacks - except maybe in very rare circumstances. Gotta remember, the attacks need to have a plausible explanation to them. You can't just say 'I attack him socially!' - you need to come up with a way to do so. Intimidation, posturing, etc. For instance, social attacks on Sue the Dinosaur would be neigh impossible as ... well? Sue isn't capable of understanding most social attacks. I might deal with this as an auto concession in these cases: They take a minor consequence of 'oblivious' (or distracted) and concede from the social combat without conceding from the physical combat.
Also, I consider social attacks to require acquaintances around to be effective. After all, the bully doesn't have much ability to embarrass you in the school yard if no ones around to watch, right? Losing a social conflict typically means losing the respect of those around you.
I'd also say the consequences of a mental defeat or a social defeat would be much different from a physical defeat.
Also, I wasn't aware that there's only one set of consequences... I'm not sure I like this. I may house rule this though... I understand that a social consequence could be used against you in a physical fight, but in my mind you should be able to take minor social and physical consequences in the same scene... or even major ones. Again, this is because losing a social conflict has different (and often less damaging) consequences than a physical conflict.
By the way, just for reference, I'm going at this to try and make my combats as realistic as possible. I like to ask my players what they want to do and then figure out how to do that within the fate rules (effectively if possible), as opposed to asking my players what fate rules they'd like to exploit. In my mind everyone should have something they can do in every conflict - whether it's the bruiser helping in social conflicts by being intimidating, the talker helping in physical conflicts be being distracting, or whatever equivalent mental conflict version. Sure, everyone will have their preferred roles, but I like the way fate works in that there should never be a time when someone sits in the corner while another player 'shines.' Fate works best when people work intelligently together to solve a problem.