All of these jsonp / iframe based instantizers have to be putting load on servers (probably not in great volume, but still). There's a reason Google had to put special consideration into how to make the ajax-endpoints scale :)
The actual video coming through is likely from a CDN, which are already built upon an infrastructure for scaling. Probably not as big of a deal as you think. Bandwidth wise it's unlikely that somebody watches the entire video as much as they rapidly hit different videos.