Competition is the driving force behind supply and demand. Through competition the market will find the saturation point where cab drivers can make a living and service is at a premium, while at the same time driving many of the lower quality drivers out. 

As for myself, I have used cabs to get to the airport at all hours for the last few decades and in all that time have never once waited 45 minutes or even close to it. There have been times when I waited longer that I wanted, but have NEVER missed a plane or even been close to missing one as a result of a cab. Further the vast majority of the time my wait is 10 minutes or less.