Exactly. One aspect of the issue is the difficulty of self-hosting video content, but another aspect is everything else YouTube does beyond hosting the file. It's a marketing and distribution platform.
Linking from your website to YouTube will let people find your Channel, getting people to come back after the one video. People can save videos for later, youtube videos will show up in search results. You want views on your website to increment the "Views" count on YouTube because that's a signal of legitimacy. You want to be able to pull one report of "how many people are watching our video content?" without having to add numbers from YouTube and your own hosting.
All of these are benefits (or lock-in) that a YouTube embed provides beyond just hosting the file. A <video> element has no way of getting most of those.
