I own pCars so I say all from personal experience with the game.
well-paced, storied campaign
It's not storied in a Need for Speed type way, it's more like Codemaster's F1 series. It has an optional progression system where you can start at karting and make it up to high downforce open wheelers (F1 knockoff cars). It is much better than Assetto Corsa's though. AC's campaign was the biggest dissapointment to me after it came out of Early Access because it is exactly like the "Challenges" section but progression-locked.
virtual currency, car ownership, customization, garage/showroom
None of the above.
diverse racing modes
Not sure what you mean by this.
cinematic event proceedings (pre-game announcers, cheering crowds, blimps, camera work, etc.)
A little bit, but not to the extent of GT or Forza.
diverse soundtrack, in-game radio controls
Soundtrack is lacking, but there is a spotify radio feature.
advanced replay controls, photo mode
Yes, it's quite expensive. Feels like they put more time into it than the actual simulation.
dynamic, reactive AI
Yes, but at the moment the AI is still shit.
working multiplayer, optional matchmaking
Yes, but don't expect a good pickup racing experience. See my comment here.
a polished user experience, which gracefully ties all of these elements together and gives the game a sense of "flow"
Yes, or at least better than AC's.
To be honest, it's a bit hard for me to judge pCars. It aims to be serious simulation, but it still handles like a simcade title. But it's not simcadey enough to contain progression elements like Forza or GT. Don't get me started on the disappointment that is the tracks, they're so inaccurate and they've butchered so many iconic tracks (most notable for me is Laguna Seca) that my enjoyment of the game is gone.