The "anonymous" setting has other effects you might not want-- unless you mean a new type of "anonymous" setting that only hides the character from account-wide friending.
I guess in addition to preferring privacy, there are other issues:
-If you unknowingly friend someone with 150 alts, your friend list becomes so long it's useless. The solution I guess is to list friends by account-name only, but I'm not sure giving out account names is good.
-There's currently no process for consent. Anyone can add you as a friend without you even knowing about it. Account-wide friending lays bare your whole list of characters to anyone who knows any of their names. If you make characters anonymous that sets up some road blocks, but people can still friend that character individually- and still without consent.