Please explain how you would do this. Because if encryption has a "backdoor", then in my opinion one cannot call it encryption or am I'm completely wrong in my understanding of encryption.
It can be encrypted all you want but the question is do you and only you control the encryption keys? Otherwise it's worthless. Many services do encrypt but also keep the keys for your convenience.
Most encryption for social media sites is transport encryption. It is asymmetric encryption such as TLS aka. SSL/https. The data is fed to the application on the backend in clear text, a backdoor could allow a copy of the clear data sent to the government as well as the real destination, i.e. the application server. It takes alot more computing power and money to wiretap data as a man in the middle.