You might have a point when different industries with different built-in subsidies compete (taxis vs. buses or trains vs. planes). That's not the case here.
A single NYC taxi medallion goes for millions of dollars: http://www.nyc.gov/html/tlc/html/about/average_medallion_pri...
Most Taxi drivers have to rent one; which is not cheap. The medallion owners get to sit on their asses in rake in the cash.
Your concern is misplaced.
That said... the Uber black car drivers are licensed, only as private limo drivers rather than taxi drivers. They're not allowed to accept street hails. (Before smartphones, this meant having an advance reservation in place.) They're perfectly qualified to drive passengers.
And unlike most regular taxis I've experienced in the SF bay, Uber drivers aren't on their cell phone during the entire drive, so they're arguably safer drivers.