The bottom-line fact is that there are straightforward methods to bypass encryption by obtaining direct access to outgoing messages before they are encrypted and incoming messages after they are decrypted (or, better yet, to simply obtain the encryption password) -- planted spyware, hidden shoulder-surf cams, collecting and interpreting electromagnetic noise, and probably other secret tricks.
These all work just fine -- for monitoring *specific targets*. They're too resource-intensive for *mass surveillance*. For mass surveillance, politicians need backdoors. Ergo, the obvious conclusion is that demands for backdoors are driven by a government desire for illegal mass surveillance, not legitimate investigation of suspicious characters.