> TOR is explicitly not private, only anonymous

It depends on how you use Tor. For example, visiting your own personal homepage and then using the same relay to visit a NSFW site would be bad OPSEC. Also, Tor comes pre-installed with HTTPS Everywhere, and you can toggle a setting that disables all http traffic if you're worried about sketchy exit nodes analyzing your plaintext traffic.

Remember: Tor can't read your mind. If you want true anonymity you have to go through extraordinary lengths to achieve it, and even then, you could make mistakes.