Right now universal summarizer is having issues summarizing unlisted videos for me, or videos with a link on youtube that is not searchable through the main page or published to user feeds. Some of these are captioned or auto-captioned. I have tried summarizing both with issues where the summarizer says the video has no captions. It would be a useful feature because there are many content creators who publish unlisted videos for Patreon subscribers.
A way I would use this feature is a way I have already been doing so, keeping personal notes on educational content with a summary. User's can also use it the way they always do, checking on a summary of the video before they watch it, just for unlisted videos as well.