Even if society was willing to exchange more privacy for a higher number of unpredictable 'negative' incidents, the question changes from what, to how many. For example, how many incidents of X magnitude would be required for people to change their minds? What if you only need 1 incident of Y magnitude to change the shape of your society in a negative way, potentially rocking its very core? Would you take the risk for your individual's privacy? You have to remember that an event can be come in different ways such as a terror attack, a semi-natural disaster, a cyber attack, an espionage that rocks the foundation of a key industry in your country, etc.
I think some of the questions society should be asking are: What is an acceptable degree of personal privacy that we should strive for? What are the blockers to ensure the material is not used for nefarious reasons? Are the right institutions in place and are they solid enough? How can society engage more and have a better understanding of the issues at hand?