I'm not sure if you would count this as a solution, but, conceivably you could "enable anonymity" at very low bandwidth ... say ... the equivalent of 9600 baud ?
This is fast enough for speech. It is not fast enough for any kind of multimedia that would be acceptable in 2014 and beyond. It might be a barrier that would cause all bad guys to use other networks, but still allow the kind of "freedom" that we're all convinced twitter gives us (and so on).