I agree that you should own the data that was created because of your interaction with the device, but I do not agree that the reason is that you own the device.

Here's an example: You go to the library (or a privately owned web cafe), and write your stories there. It doesn't matter that you don't own the device. It's still your data.

I don't think that analogy holds up. Maybe: does the typewriter manufacturer own meta data such as letter frequency, average work length, etc that their product calculates based on your usage?

No, of course not.

Once money exchanged hands, it's not their product, it's mine, as is _all_ of its output, including logs, etc.

Otherwise, I'd call it 'spyware'.

This already isn't the case in many instances where you don't actually "own" the thing, you just have a license to use it.