I stick to Taiwan Taxi, Tafong, or any other big company. First of all, as part of a company, you can call the managers and complain if service is amiss. Also, they have company provided GPS, meaning that if they do not know the address, they look it up. No driving around lost in space....wasting time and money. Moreover, if I lose something, at least I know which company it was -tell me if we ever pay attention to the cabbie's name or number.
Tafong is right around the corner for me, so I can book longer trips -Yilan, airport, hire a van- with an agreed upon price.
Taiwan taxi now has an app, so calling them is one touch away, a la Uber.
Taxis and doctors have both the same problem: compared to our own Western countries, service is quick and cheap, but they suffer for it. The rush is a killer, literally, and yes, there are many trying to make a better buck out of cheating. Hours are long and teh job is thankless.