There is no need to be afraid of the video.
I don't think YC cares at all about how good of a speaker you are, they probably have a million applications and they just want to have a first look at the team.
For example, if you live in the same area but you don't even manage to gather and shoot a one minute matter-of-fact video that explicitly asks to avoid wasting time on it, then it'll be hard to believe that that team will be able to survive the pressure of a startup in its first couple of years.
Also, I think that in a startup environment you have to be ready sometimes to just quickly do things, and the video is a way to show that you don't need to invest three days scripting it and shooting it, but just half an hour making sure your words are audible and such.
What other startups say doesn't really matter. Startups don't have to try to guess how successful 1000 teams may be. YC has to.