I find that comforting. In fact, if I was a large organization and processed a ton of user data, I'd want to store that data anonymously too, due to the sheer risk of having that personal data.
And then you have users who always go to the same PF Changs but use navigation in case there is traffic and they should use an alternate route. Your competitor app will learn this and adapt and yours won't. The average customer will have no idea you aren't storing their data and likely doesn't even care while they aren't reading an article about privacy. While I personally wish everyone were to take your approach is also tying one arm behind your back.
Edit: I once worked with an ex-googler who told me to always store all the data you have because you never know what you can use it for, you can't get it back if you change your mind and storage is cheap. Hard to argue with this if it's "just" about competitive advantage and monetization.