Who do you trust to know the metadata about how encrypted messages are flowing?
Who do you trust to get the crypto implementation details right?
How will you support use of multiple devices? People generally expect seamless switching between phone and laptop these days.
In fact encrypted messages could be stored publically anywhere and only the intended recipient could read them.
The flow of messages is not encrypted, the system only encrypts message contents. (However, there are options to make it very difficult to trace, but that is a different issue.)
Trust is up to the user to decide and is always necessary.
Multiple devices is easy enough, a device can encrypt its own private key and send it to another device (using the target devices public key). The target device would now have 2 private keys for decryption.