While I agree that every point of schroeder's response is true, there are two deeper issues that make it so much more dangerous than the current model of security. Right now, if you install an encryption key on a system, that key only controls your system and can only be accessed by the people you trust to access your system.
Breaking into any system is a question of economics to any would be attacker. Let's say for example, that your system is a database of 5000 clients with 5 users who can access it from a single network. A hacker has very few possible access points to try to exploit, and the odds of him finding a misconfiguration are relatively small; so, they need to ask themselves if they can spend little enough time and money getting into your system to make those 5000 client records worth their investment. If this network was set up by a mostly competent person, the answer is probably no.
A national back-door could be just as well encrypted, but it would expose hundreds of millions of devices to thousands of law enforcement agents. Hundreds of separate networks will be set up by sysadmins of various skill levels. Many of the cops you trust to access the system will not be properly trained in cyber security. In this case, a hacker only needs to target one of the many, many people, devices, or networks who create these weak links. This makes intruding on the system several orders of magnitude easier, while making the pay off several orders of magnitude greater.
In fact, the payoff is so much greater, it would be worth it to many hackers and national governments to go through the training process of joining law enforcement just with the goal of gaining access to this system.