I think this would be very difficult since almost everyone wants to be able to play a video on their phone. Even if you don't have any video apps on your phone, you can still just as easily play one through the browser. What if someone uses a URL shortener and you click on it and it goes to youtube? IDK if there is a way to block websites, but the list of of sites dedicated to videos is pretty long.
Perhaps if the OP explained why videos are never an option, it would help narrow down the solution.