in this beta you included a in-client video player. Maybe it would be a nice feature to synchronize video playback with every client (like Watch2gether.com). I often watch videos together with friends, while talking in Teamspeak. It would highlight Teamspeak’s capabilities as a social plattform to hang out in general.
I don’t think that TeamSpeak should be overloaded with a dozen integrated features that could simply be an add-on for those that actually need it.
You already mentioned a platform that does the thing you asked for very well as it was designed for just that purpose.
TeamSpeak was designed for communication, not entertainment. And that’s what they should focus on.