There are definite UX "costs" to following a Youtube link rather than watching an embedded video: it breaks the reading flow, it distances you from the context that the embedding site often provides, it opens a separate tab or window that you'll need to manage, you need to wait for the Youtube page to load, etc. These might seem like minor things but watching videos is often an impulse act, so any operational or psychological obstacle to the user acting on that impulse makes it less likely that they'll follow through. And the opposite is true too; an embedded video is more visually interesting (think of the still frame) than a generic link, making it more likely that you'll bother to actually watch the video.

There's also a cost to the embedding site -- embedded videos keep the viewer's attention local, whereas linked videos send them offsite, possibly never to return. Many sites will just pick something different to embed rather than risk losing the viewer to the endless morass of distracting content on Youtube.