So either the traffic patterns allow pickup to be optimized to do much better than doubling the car-miles, or traffic patterns are so that it doesn't matter.
(of course that's overly simplistic, but I don't see how it's a less valid simplification than yours)
The important case of commuting toward the city is interesting. Car-sharing breaks completely there - everybody starts work at about the same time (commute traffic confirms this). So we'll need as many shared cars as we already have. No savings at all.
Any savings comes down to off-commute traffic. Its a second-order effect. Maybe even too insignificant to bother with the complexity of sharing.
If people are going from everywhere to everywhere, there will be almost no extra cars.
Yeah, when all directions are congested it will add a lot of very short trips.
Something interesting to think about is logistics optimization. I have nothing against the big brown trucks but it should somehow be possible to haul my amazon packages from distribution center in the city by the railroad tracks to the burbs. Or distro center to distro center package movement.