You may well be right - But I use two browsers simultaneously most of the time, one of them doesn't have me logged into YT and the videos play the same as the other browser where I am logged-in. How is that different to LE not being logged-in and requesting to play a video?
You need to log a ticket with the add-on developer, as LE doesn't maintain the YouTube add-on.
Tubed is another add-on you can check out, it uses a shared API key that is already embedded in the add-on, it's written by the same person who maintains the YouTube add-on.
GitHub - anxdpanic/plugin.video.youtube: Watch your favorite YouTube content on Kodi
Watch your favorite YouTube content on Kodi. Contribute to anxdpanic/plugin.video.youtube development by creating an account on GitHub.
github.com