When is a trust-level-badge-related user title set or not?

I meant, the title attributed to the Trust Level badge is added to the list of titles that they can select, in a dropdown under /my/preferences/account. They can select it anytime after getting the badge. Whether they do select it or not, is another matter.

That would be because the Leader never changed their title when they were promoted, so it remained at their current title (Regular).

It would be difficult to automate it, because what if they attain a badge that gives a title (like Champion), and get promoted? What will the title be automatically set to then?