I use Uber in the DFW area on a regular basis, including rides from and to the airport, as well as other cities/towns in the area. I've never had a problem with short rides, and I don't think I've ever waited more than 10 minutes at the curb at the airport.

As one data point, I live in an urban residential neighborhood in Fort Worth, and commute to downtown, almost exactly a three mile drive. The wait to be picked up is usually 3-5 minutes, and I've never had a driver seem upset about the short ride, much less say anything. You'll be perfectly okay using Uber to get around here.