If it's not client-side encryption (where only you know the password and the stuff is encrypted on your machine before it is sent), then it's a non-starter. The government can just order Google to bypass the protections for their suspect.
I understand that's your legal theory. The article says, however, that remains an "unanswered legal question" in the United States, according to Jennifer Granick at Stanford's CIS.
And even if it's client-side encrypted, unless the client is open source there's no practical way to know whether there are backdoors, or whether a future update adds backdoors.
If they control the code they can bypass the protections for their suspect as well.