Is a total elimination better or worse than a reduction? I don't have an answer, and I see good arguments for each side...
This will happen sooner or later and for sure there will be companies and individuals that will be affected by the change, but that is not enough reason to stop the development. And this is not Uber specific topic either. If not Uber, some other company will one day work on this.
I hope Uber pay their taxes.
Think about this problem from Uber's perspective. More than two thirds of a fare go to the driver in most cases. Let's say eliminating the driver allows them to cut prices by 50% to account for purchasing a crapload of cars. Now imagine someone else builds self-driving technology (or licenses it) and copies the Uber business model.
A competitor building self-driving cars for-hire is instantly cheaper by a ridiculous margin. Uber would be overtaken by this competition in no time at all. This is unquestionably inevitable. Uber can't say "pay double (or more) so we can take the moral high ground and employ a bunch of fallible humans" because a.) humans are worse drivers than computers and b.) humans just cost more and nobody would pay to have a human driver.
Additionally, if Uber ever goes public, they're legally obligated to maximize return for investors. You can't keep human drivers around as a purely feel-good exercise.
A lot of business models do. Horse carriages eliminated income of (most of) manual porters, and cars eliminated income of (most of) horse drivers.
Unless you are a worshipper of Ned Ludd, that's how technologies work and will always work. Something new replaces something old, and people whose income depended on the old stuff have to look for different income.
I am pretty confident self driving cars are going to create more jobs than they destroy. Whole new businesses will be economically viable once the transportation costs are super low, traffic is less of a problem and when you don't need parking. On demand economy 2.0.
I'm definitely interested to see how this iteration plays out over the next few decades.
[1] http://www.ers.usda.gov/media/259572/eib3_1_.pdf [2] https://en.wikipedia.org/wiki/Technological_unemployment
Its business model was sacrificing someone's income in the middle to be cheaper than ordinary taxis. But with self driving cars, they can minimize the costs without hurting anyone.
Really really smart and huge move at the same time. Whoever pushed this idea in the company deserves a huge credit.