The superior alternative is to avoid sharing sensitive datasets and avoid keeping data whenever possible. No such alternative exists for many applications of cryptography.
But we live in an era where organizations find our private data impossibly tempting and are content to sacrifice the rights of individuals so long as they can't fight back. This research gives such entities the excuse to build tools that should not be built and publish data that should not be published. By saying "OK now it's safe (if you did everything right)" rather than "don't do that", it is the enabler of future privacy fiascos.
The answer, if there is one, is probably legislative: hold entities criminally liable for data breach. Should such legislation pass, I wonder how much interest in this research will wane.