This has become more critical of late, as Google has introduced some change in their embedding logic which now causes youtube embeds to throw a 153 error when users are logged in to their Google accounts, forcing them to click on the embed to open the video in a new tab, cf. e.g. this Reddit post: Reddit - Please wait for verification
This is issue can be fixed by converting the link in the iframe from youtube.com to youtube-nocookie.com . Whatever UX disadvantage comes from not having the video contribute to your view history is surely outweighed by being able to actually view it as an embed, so the option to convert embed links accordingly would be much appreciated.