How does Uber improve "the amount of car pooling we do" in a significantly useful way (i.e., one that furthers the goals for which car pooling is usually advocated)?
Consider if an individual leaves their home, drives 8 miles to their destination, and later returns home driving another 8 miles. Total miles of pollution and "road space" is 16 miles worth.
Suppose that same individual uses Uber using the same type of car. Obviously the same 16 miles would be traversed - but even then, the car weighs slightly more so would consume slightly more fuel and produce slightly more greenhouse gasses. But, in addition, an Uber driver will almost always have to drive from wherever they are TO the customer's location to pick them up and have no one else in the car during that time - and this scenario repeats on both the outbound and the inbound trip. Suppose that, on the average in that area, the Uber driver "deadheads" three miles on each trip. Now we an additional six miles of driving and associated environmental impact (including road congestion).
Sure, in the 'self driver' case, there's 0 miles of dual occupancy (a.k.a. carpooling) while in the Uber case there's 16 miles of dual occupancy (with slightly higher pollution due to the additional 150 or so pounds resulting from dual occupancy) -- but the cost is an additional six miles of single occupancy.
About the only "carpooling" type benefit is that less space needs to be devoted to parking at the destination if enough people take taxis, Uber, public transport, cycle etc...
If the goal is to increase average vehicle occupancy, why don't we just pay people to pile into cars and then drive the cars in circles?