|These kittens don't violate YouTube's|
TOS and we shouldn't either :)
Downloading videos from YouTube through a third-party service is a violation of section 4 of YouTube's terms of service. I don't want students thinking they can download anything they want without concern for copyright or a company's terms of service. Therefore, I think I should model for students the behavior of respecting copyright and a company's terms of service.
In addition to the copyright and TOS violations, the other concern with downloading YouTube videos through a third-party tool is the varying quality and reliability of those tools. That is of particular concern when you start to dive into the free services promising that function because while they may work, they may also offer a bunch of malware to go along with the video file.
I understand the tough position that teachers find themselves in when YouTube is blocked in their schools and there is a video on YouTube that they would really like to share with their students. I've been there, it is frustrating. My recommendation at this time is to talk to your administrators about using YouTube for Schools if you cannot convince them to allow teachers to access YouTube directly.