It should be perfectly clear that the client-side impact of this transfer is not important, since a mobile device still loads YouTube embeds instantly, but does not burst into flames while doing so, as it necessarily would if the energy cost was as high as the other person is suggesting.
Sure, TBH I was inspired by your comment that "there is a person whose full-time job is to consider the energy usage of YouTube in all its aspects" and figured I'd throw in an IEA commentary from someone who watches the watchers.
It's a big picture look at youtube energy use, but hopefully of tangential interest.
