As follow-up, I used the hotel's car service from the airport (I know, I know).
Just for jollies I opened up the Uber app a few times whilst at my hotel (Wangfujing). At certain times of day I'd see a few cars roaming around nearby on the map, however when I left the hotel finally at 7am Monday morning the app could not detect a single car anywhere. I took a taxi - 30 minutes and Y100.