What bothers law enforcement is simply the idea that there is something they can never have access to. The reality is that it has always been that way. Two conspirators could walk into a pub and sit a corner booth in the days before ubiquitous electronics and the law would never have access to that conversation.

There is nothing about the advent of new communications technologies that gives governments the authority to mandate circumventions for them. It's a attempt to preserve a status quo that never existed.