No. People will always trade personal comfort for convenience and price. Look at airlines. Back in the 70s, a flight was a great pleasure. Then the airlines were deregulated. As it turned out, people didn't care nearly as much about their legroom and on-board meals as they cared about price. That's why nowadays, flying coach is generally uncomfortable, but also cheap.
And in that regard, Uber has a huge advantage: UberX is much cheaper than a taxi. In Chicago, a taxi+tip costs about 3x more than UberX (with Pool). It's similar in many other cities. That's the big advantage that UberX has on taxis.
Indeed, Uber's pricing is getting competitive with public transit -- in Chicago, UberX (Pool) is only 2x or 3x more expensive than public transit for a given distance, but much more comfortable (regardless of the niceness of the car) and much faster than public transit.
For UberX, the drivers and cars could be awful. It wouldn't matter. What matters is that UberX occupies a sweet spot in terms of pricing and speed that neither taxis nor public transit can match. Consumers value pricing and speed far above comfort.