If it takes you more than 30 seconds to come to "An app that allows anonymous public messages on a social network currently wracked by abuse is not a good idea", you haven't been thinking.
I think you're confusing "anonymous" with "uncensored". Nothing prevents these messages from being filtered for abuse.
Not to mention that being a single account, and hence easily blocked, the potential for abuse is minimal compared to the alternative of simply creating a new Twitter account, which would be just as anonymous.
