Francois,
I'm so happy to hear that I'm not the only one waiting for a decent solution to this. I've already put in a feature request which you can vote for here:
https://community.canvaslms.com/ideas/1639. The feature request is not limited to video, and maybe it needs to be renamed so that people can understand what we want without having to read the comment thread. I'm open to suggestions.
In the meantime, there are two things you can do today. The first is to let Canvas compress your video, and store it in their video file system rather than your course or personal files. To do that, follow these instructions:
https://community.canvaslms.com/docs/DOC-1867
That works well for low resolution video, but you really need to to test the quality of each video. If you need students to be able to see detail in your video, you aren't going to be happy.
I was very excited when I discovered the second work-around, and I even used it to create an LTI editor button for those who are afraid of tags. But, I have to say, I have seen this fail, so I don't completely trust it. For what it's worth, here is the blog post I wrote when I first learned about this trick: