Facebook is a powerhouse when it comes to content and marketers are constantly working to keep up strategies that work best for getting engagement. It doesn't matter if it's a link to a Youtube Video, your company website, Vimeo, or LinkedIn - you're going to get a less than ideal response.
We posted the same video on Facebook using direct upload and then with just the link to show the difference between the two.
The image on the left is the one uploaded directly, and the one on the right is a YouTube link.
The one on the left looks much more inviting and has a play button right on the video. With users short attention span, you want to make it as simple as possible for your users to engage with your content.
If your goal is video SEO or to get your Facebook audience over to engage with YouTube content, directly posting to Facebook might not even be your best option. Since Facebook is designed to highlight and prioritize visual content, you can take a screenshot of the Youtube video and post that as an image. With this, people still see the play button which works as a draw to watch the video, you get to choose the exact frame that catches attention, and leverage the boost of having an image in your post. Even if someone clicks on the image and it goes full screen and realizes it's not a video, hopefully, that click they invested will lead them to go actually watch the video.
It's important to pay attention to your analytics dashboard to see how certain posts are performing. Feel free to experiment using different content with directly posting videos, posting as a link, or posting a screenshot.