The YouTube addon for Kodi maintains most of the website’s functionality (and actually improves on it in some ways) but it’s not perfect. For instance, you can’t add videos to custom playlists.
There is a workaround, though. If you right-click a video, you can choose to add it to the queue or the Favorites playlist. This isn’t ideal, but it does let users find videos again later so they can add them to the playlist they actually wanted.