Transcribing locally isn't free though, it should result in a noticeable increase in battery usage. Inspecting the processes running on the phone would show something using considerable CPU. After transcribing the data would still need to be sent somewhere, which could be seen by inspecting network traffic.

If this really is something that is happening, I am just very surprised that there is no hard evidence of it.

Even the parent's envelope math is approachable.

With their assumptions, you can log the entire globe for $1.6 billion/day (= $0.02/hr * 16 awake hours * 5 billion unique smartphone users). This is the upper end.