YouTube for Schools has partially contributed to that trend. Tools like ViewPure and Watchkin have made using YouTube videos in schools a little less scary too. All that said, there are still lots of schools that block access to YouTube. That's why a few years ago I started to maintain a list of alternatives to YouTube.
This week I updated my list of alternatives to YouTube. I removed some options that have disappeared and edited information about sites that have changed. The updated list and video search engine can be found here.