The problem here is that tor is largely focused on realtime communications, and stuffing packets through e.g. facebook chat would probably be too slow. It would work great for another anonymity network that was more message-focused with no realtime needs.

That said, you might be interested in tor's meek pluggable transport: https://trac.torproject.org/projects/tor/wiki/doc/meek

Essentially, the idea is that someone buys a VPS hosted on a cloud service with common ingress IPs (such as Google App Engine, Microsoft Azure, etc). Tor clients then connect to it, sending an innocent-looking domain (gmail.com or something) in the TLS SNI header, and then only in the datastream protected by TLS do they expose the tor protocol.

This is of course useless against NSA and GCHQ, which have access to all these cloud providers, but it's very useful for example for people behind restrictive country-level firewalls as the authorities are reluctant to block such large services and it's hard for them to distinguish this from normal traffic.