It's entirely free, almost entirely grassroots (governments occasionally ask that the pick-ups/drop-offs move slightly), and remarkably safe (1 known incident in >30 years). Having grown up in the area, I was surprised when I casually made reference to it to someone not in the area and they had no idea what I was talking about.
Anyway the number of cars queued up to cross the bridge to the east in the afternoon strongly suggests that road is underpriced.
I'm not looking for an answer here because I know the answer. The answer is that car drivers are the most self-entitled bunch of externalists the world has ever seen. If there was any sense in this system the toll at the existing toll plaza on the Bay Bridge would have been raised until congestion disappears, but that hasn't happened. On the other hand BART fares are indexed to inflation, because only the riff-raff ride transit.
It's that informal and inconsistent group knowledge that gets turned into an app, which formalizes the informal parts, removes the barrier to entry (knowing about the informalities in the first place), and (should) build protections in to ensure conformity to the now established system (payment, insurance, etc).
1. To get from the East Bay to SF in the carpool lane you need 2 passengers (3 people total - or a car that only seats two)
2. The East Bay already has a pretty nice system for this called the Casual Carpool which is probably its biggest competition. The Casual Carpool is just a bunch of spots (usually BART Stations) where drivers can stop and pick up a few other passengers to get in the carpool lane across the bridge and usually the passengers chip in a few bucks for the toll. This system is pretty good and works well considering the need for 3 folks in the car to get carpool lane access. The Lyft model is a lot harder to coordinate picking up 3. The biggest issues with Casual Carpool are that there's no revenue for the driver and it's mostly one way (inbound in the morning). The eastbound after work system is not as efficient, there's a common pickup area downtown with stops indicating destinations but it can be hit or miss on whether passengers are there when you're ready to go home.
Long and short of it I think this is a Peninsula solution not really an East Bay to SF one yet.