1. Advice site. Some people coming for help, often suffering mental illness or extreme emotional conditions. Presence of highly volatile individuals could ruin the experience.
2. Trust & Anonymity. Many people come here sharing deeply personal issues. They can do this because they are anonymous and do not need to worry about negative reprocussions for sharing. Video chat would erode that to some extent.
I do support the presence of a chat-like functionality for the purpose of talking about a question or problem with someone, but I don't think video information is necessary to do that.
It may seem good but imagine all the weirdo guys who would be sending videochats to girls? @lumos had posted a collage of the weirdos messaging her. I think it would be both good & bad, but a bit aggravating for some girls who are always been harassed.