There are many caveats* to consider when routing through Tor. It would be a bad idea to just silently do so when the user engages private mode. Incorporating Tor as a 'super-private' mode or whatever would be great, but it should be possible to use normal private mode without it.

*In particular the information that you share with the exit node. Especially if you're not aware you're using Tor, it would be easy to share identifiable information.