Not a problem we have as we live nearly half an hour away from the airport, but clearly it is a big problem for some who live close by. Taxi drivers may have been waiting in the holding area for an hour before being allowed to approach the pick up point, and then they only get a short fare. I'm afraid they must just view it as the luck of the draw. They have no right to refuse a fare without good cause, such as a person being dirty, drunk etc.
From The Age:
Dozens of taxi drivers have been fined in a police sting for refusing to take short fares from Melbourne Airport.
I don't catch cabs very often, but here is my theory. I did put this into practice once. Some people are rather timid about catching a cab and ask the driver if he or she can take them to such and such place. That is not the way to do it. I walk up to the taxi, open the rear left door, get in, greet the driver and tell them where I want to go. At times they will have the doors locked as happened to me once. I tried the door handle and it was locked and the cab driver did not seem to want to open the door, I guess wanting to filter so that he received a good fare, so I went to the cab behind and got in that one. What I should have done is taken a photo of the taxi number and the registration plate, but this was in the days before cameras in phones were widespread.
If you are in a taxi and the driver refuses to take you, photograph his or her ID and once out of the car, the car registration and the taxi number, and note the exact time and I think the reporting process is quite simple. One report from one member of the public is not going to have a great effect, but if reports mount up about a particular driver, then there will be trouble for him or her.
Fine in theory, but if the highway patrol in plain clothes can't get taken to where they want to go, what hope for anyone.