I think the question is still valid what you actually do with them once they are saved.
Much of the knowledge of writing the software is manifest and captured in those chats. and we share them so that we can learn from each other.
I work in data and machine learning, it's pretty common to attach artifacts like charts, images, data outputs to a PR for me, but not include them in the codebase.
I'd only want to do that if it was going to be useful at some future point - do you go back to chats / transcripts etc months after a PR is merged to understand its design? (that sounds rhetorical, but I promise it's a genuine question!)
Why don't your chatbots just write clear, well documented code?