You need to persuade people to invest.
You need to persuade people to work for you, good people especially, in the early stages when maybe you can't pay as much as other people or you can't promise a stable career path.
You need to persuade customers to buy your product, or if you don't sell it directly you have to convince store fronts, manufacturers, and the whole gamut that they're taking a justified risk on you.
And yes, when you go onto the Ycombinator forums to complain about their approval process you need to persuade readers that you have a point.
Having social anxiety, or a distinct lack of charisma will interfere with all of these.
Really, all I'd like to see is some sort of other avenue through YC that doesn't necessarily require a video to be posted since that adds to a particular sort of bias.