The issue stems from having a fixed width on the video. When you embed from YouTube, the embed code specifies a width and height for the video. Now there is the possibility to have the width flexible to the viewport size and the height then calculated from the width; since you would want to keep the aspect ratio intact.
If third party modules are playing the video with the built-in video player, then if we have dynamic sized videos in the core, then it may be possible for third party module to enjoy that feature; if not, then it would be up to the module developer to have that feature.
Since we are on the topic of video playing; I worked on videos a lot for a client with Dolphin. One thing that is easy to do is to adjust the video player for vertical videos; idiots are going to be idiots, they are going to continue to take vertical videos. Instead of having a small vertical video with bands on either side of the video, you adjust the video player to the width of the vertical video. You know if the video is vertical when you check and see the width of the video is smaller than the height. I have that code somewhere; I can try and dig it up. It does make viewing vertical videos more enjoyable and if you have a site with members on phones uploading videos, you are going to have a lot of vertical videos.
Yes that is the problem that i don't want to come across with.