It is definitely possible, at least for videos that have a transcript. There are tools to download the transcript which can be fed into an LLM to be summarized.
I tried it here with excellent results: https://programming.dev/post/158037 - see the post description!
See also the conversation: https://chat.openai.com/share/b7d6ac4f-0756-4944-802e-7c63fbd7493f
I used GPT-4 for this post, which is miles ahead of GPT-3.5, but it would be prohibitively expensive (for me) to use it for a publicly available bot. I also asked it to generate a longer summary with subheadings instead of a TLDR.
The real question is if it is legal to programmatically download video transcripts this way. But theoretically it is entire possible, even easy.
It doesn't work yet, the screenshots are from a private test instance.