Nowhere to park. Also, they want to be close to the "good" places so they get picked when a rider shows up.
Induced demand and congestion are complex. A taxi is probably better than a car, but neither cars or taxis have enough capacity to viably challenge congestion. You need mass transit that runs frequently and isn't stuck behind cars.
There's still congestion to deal with, but a bunch of people whose main work has no set hours who can go 'it's raining, time to taxi some people who don't want to walk or cycle today' synergises well with active transport and transit.
Cities already have absolutely massive amounts of their real estate dedicated to parking. The answer to this problem is not and never will be “more of the stuff that’s causing the problem”.
The question was why they stay on the road when they're not delivering someone. If the issue isn't lack of parking, what is it?
The commuter and residential parking doesn't free up for Uber drivers if it's not being used by its primary customers.
Disclosure: Extrapolating from how it works in my town.
If they travel by taxi there's only one car on the road - but the taxi has to do a third trip, going back from the city to the suburbs between passengers. That trip is likely to be made without a passenger - because in the morning rush hour, far more people want to go in one direction than the other.
Of course, in some cases taxis may help reduce congestion - transporting people to and from train stations, and allowing people who usually cycle to transport bulky items, might enable more car-free living.