If you make a recording, you might have made some small mistakes, like typing a few words incorrectly.
Once you upload it, there is no way to edit the content other than downloading it, changing the content and re-uploading it. If you have already embedded the recording in a website, making this edits become time consuming (download, edit, re-upload, update cast-id in website, etc).
It is also true you should validate the content before uploading but maybe some viewer catches an error later. It also seems easy to implement: adding a text input with scrollbar to the edit section that loads the recording content and then when save, the file is modified.
This would probably need to deny too large files. Also it needs consideration if the user adds invalid content what to do in that case.
The edit page i’m referring too is:
https://asciinema.org/a/<cast-id>/edit