I think that the threshold of user hover-boxes should appear in the privileges page as it is a privilege.
I do not think so. This is not a privilege, it is a customisation bonus. Privileges relates to actions that impacts the community (open/close up/down votes, protect question, moderator tools, flag, ...). Profile does not.
Reduced advertising defies this statement. But this is a huge improvement in the user experience on the stacks sites. I think user cards does not deserves such a highlight.
I agree. If reduced advertising is there, the user card should also be.
It is where people will look for it, and adding it will prevent a lot of questions or confusion.
Further research reveals it is already on the Established User page, which a somewhat good place as long as it is displayed at 1000 reputation.