The actual study modeled a 40% reduction in number of taxis on the road when hailing was made more efficient, with carpooling passengers, and a re-purposing of parking space:

In the 2010s, the Senseable City Lab at the Massachusetts Institute of Technology, where one of us serves as the director, was at the forefront of using Big Data to study how ride-hailing and ride-sharing could make our streets cleaner and more efficient. The findings appeared to be astonishing: With minimal delays to passengers, we could match riders and reduce the size of New York City taxi fleets by 40%. More people could get around in fewer cars for less money. We could reduce car ownership, and free up curbs and parking lots for new uses.

But it turns out that just like with widening highways, human behavior responds to the increased efficiency by stepping up the demand to reach the previous equilibrium again.

I imagine that the fact that you call cars with an app instead of waiting for an empty taxi to pass by is more efficient, and you can have less cars for the same number of passengers. Basically having less empty taxis on the road.

I know it's a stretch, but this is the only way I can see Uber reducing traffic.

Because mainstream media said so!

Tbf uber pool DID help in theory alleviate a bit of traffic but americans are allergic to sharing rides. And even then buses are several times more efficient.