I suspect the persuasiveness in oral communication is related to our susceptibility to favorable impressions of people who mimic our tone, posture, etc.

The non-verbal communication component should probably also be taken into acccount. Face to face discussions can be more dense of information, since tone and posture can also communicate nuances of beliefs and confidence in them that can make one's position more clear (and often more acceptable). Written communication is very often pretty dry in this respect, resulting sometimes in flame wars and people becoming only more stubborn.