Hi foxview,
Thank you for your post.
Currently, it is not available to delete the whole conversion of one-person private chat except for hide/archive. We have seen lots of customers raise the same concerns as yours at Teams UserVoice
Delete Private Chat threads. Based on the related engineer, the deletion of private chat threads is on the back log.
We are sorry for your inconvenience and hope you could understand situation You could post a comment or vote on this Teams UserVoice website, some features might not be considered until many customers
demand for them. The related development team is monitoring your feedback there, your voice is helpful for better using experience.
Thanks for your understanding and time.
Kind Regards,
George