In the case of video, videos take up a lot of space and transcoding (I believe) is complicated and resource-intensive. I understand people not wanting to roll that themselves, especially when there are free options
Embedding is the easy, lazy, biz-dev-promoted, and copyright-friendly option.
The longer-term risks are the counterargument.
Storage costs of even video, for curated content, are de minimis. That's changed over the past 10--15 years (roughly an order-of-magnitude decrease every 3 years or so). Bandwidth is more substantial, but CDNs can address that w/o the third-party domain list. E.g., "example.com" points "cdn.example.com" to their CDN provider. So long as Example maintains control over their own domain, third-party reregistration isn't a threat.
(Well, until your portfolio of redirects extends to the thousands or millions of domains. Scale has problems all its own.)
