Eh, but it would work inside Google Maps/Waze. Some people I know use Google Maps or Waze every day, despite knowing what the best way to get to work is. This means Google likely already has the "driver" supply, and just needs to find a good way to provide those drivers with appropriate passengers.
So when someone first opens Waze/GM, you could put up a notification: "Dakota Doe <picture, rating> is 2 minutes away and is also trying to go to X. Would you like to carpool them?" People who say yes get pushed it more and more often, people who say no get a screen the next time they open the app expounding on the benefits of carpooling.
The feature they're describing sounds like a good fit for Google Now. I don't know what "stock" is well enough to know whether Now counts, but Now definitely has tight integration with other Google services already; if RideWith appeared in there, it probably wouldn't raise many eyebrows.
And what if they add a button to Google Maps that showed a shared car? And tapping it started the on-boarding for a ride-sharing service. Completely opt-in.
So when someone first opens Waze/GM, you could put up a notification: "Dakota Doe <picture, rating> is 2 minutes away and is also trying to go to X. Would you like to carpool them?" People who say yes get pushed it more and more often, people who say no get a screen the next time they open the app expounding on the benefits of carpooling.