Taglines that come from the short bio field in author are dynamically generated when the story is launched. Therefore it is impossible to have an old tagline persist on a story and have new stories use the updated short bio field for a new tagline. This is similar to SB-I-500 for author names. If the author changes their name and wants the tagline to reflect the new name going forward while keeping the old author name and tagline in previous stories there is no way to do this.
Thanks for the suggestion (and the related author name Idea).
We don't have near-term plans on this front but will keep this in mind as we plot the future of the Publishing Platform.