I'm a big believer in fully anonymous communication. Unfortunately, we live in a censorious age. Those who enable anonymous communication frequently become the targets of legal and social pressure exerted by angry mobs, mobs mostly composed of people who aren't even trying to communicate anonymously. Yik Yak fell in part because, instead of listening to their users, they listened to people who weren't their users.
The next Yik Yak needs to be fully decentralized --- with anonymous development, so there's nobody to sue --- and with a network architecture that resists technical blocking attempts. The next Yik Yak needs to treat censors as adversaries, not partners. Only this approach can bring anonymous communication to its full potential.