Oh, another reason I realized you should have registration/people's email: While you wouldn't want to automatically send these people marketing emails without their express interest, you WOULD want to be able to send your free tier users security notices.
I don't know which API you are at, but I use OpenWeatherMap, and usually, do so with a city ID to request the location. But you can query OpenWeatherMap by GPS (I don't, myself), and you could be querying it using precise coordinates. So if OpenWeatherMap were to have a security breach, my location history might be leaked, and I'd like to know that... even if I'm on the free tier.