I know quite a few teachers who don't like their introduction videos but put one up with the application because it is required. My guess is some take it down or make it private/unlisted once they have a reliable base of customers and don't actively need new students. 

What surprises me more are videos where the teacher is not present. I've looked at a few profiles that have entirely audio presentations, which surprised me because italki has  a rule about appearing in the video, and besides, most students can get a better sense of what the teacher is like and how expressive she/is visually from a video. I guess italki makes exceptions for some situations.

@Sophie I remember that italki includes Youku among the suggestions for video hosting services, is that a viable option?

See: https://support.italki.com/hc/en-us/search?utf8=%E2%9C%93&query=youku