This idea comes up in the context of my research into bot accounts throughout Wikimedia. Right now I can find bot usernames, but there is no programmatic way to get the bot operators' usernames from this. It would be nice to be able to programmatically ascertain bot "ownership" directly through the API.
One way this can happen is by making it possible for accounts to be formally "associated" with one another. For instance, I can flag that user "Harej bot" is associated with my own account, "Harej." This can also be used for legitimate alternate accounts; I can say that "Harej (WMF)" is an alternate account of "Harej". Associating two accounts would require proving having control over both.
In my mind this would be a one-to-many relationship; one account can control many others, but a given account cannot have many controllers. In addition to being able to figure out relationships between accounts through the API, this could enable certain "power user" features such as being able to switch between accounts via a menu. (There shouldn't be concerns of sockpuppeting, since account associations would be public.)