The central problem with mandating backdoors is that the same math that can be used to launch a secret plot is the math that protects our medical and academic records. It’s the same math that keeps credit fraud and identity theft at manageable levels. Every demand that services keep plaintext is an opportunity for criminal organizations to steal valuable information. Every algorithmic weakness can be exploited by an organization with botnets or willing to invest in cluster.
Then there’s the whole spectre of cyberterrorism.