The UX for saving and sharing videos is the same as for images, including right click to save. You and I don't get that UX, though, because Twitter, Google, Facebook, Netflix, and most websites write code to fight off-site sharing and deploy it on their videos but not their images. They skip images presumably because it's easier to bypass there and because everybody knows you're user-hostile when you break image UX, whereas when you break video UX even HN users blame the browser or operating system.

So it's worse than a UX problem, it's a social problem.

Maybe as-easy-as-screenshots screen recording would go a long way toward solving it, but we've been beat to it: big tech has bent kernels, operating systems, browsers, and even most nations around the world into collaborating to refuse to take moving screenshots of video files, under the label of DRM.

So maybe the root of it all is just timing. Images were added to the web when the web was just a tool, so everybody knew what they were before big tech could set an expectations like that moving an image from memory to disk isn't a normal feature, or that wanting to is controversial, or that doing it might be illegal. Video, though, came at a time when there were big players that knew the stakes and were ready.