edit: I only meant this in so much that it's entirely possible for Google, that controls both Chrome (the biggest browser) and YouTube (biggest online video site) to encable DHCP restrictions on video capture from within the browser for sites (such as YouTube) that might implement it. Given their proclivity towards giving the RIAA/MPAA whatever they ask for, it wouldn't surprise me.
I'm pretty sure that encrypted media sites already use HDCP because my projector glitches for a few seconds sometimes when I first navigate to Prime Video, and whenever I have a secondary analog VGA monitor connected Prime Video will only play in standard definition.
There's fair use though. It makes sense that you are able to quote a video. Its just that those people on Twitch don't quote; they play the whole thing. Captions with bookmarks would fix that (Pornhub has that natively, quite useful).