Eh? Songshan mainly serves the people of Taipei so they can go and clog up other parts of the island, like Hualien and Taidong and the outlying islands. People from Taidong and Hualien usually take the train - and for international flights, the people of Taidong often travel to Kaohsiung airport.
Songshan airport mostly caters for the travel requirements of people in Taipei, not the rest of the island.
Moving the service Songshan offers will likely cut tourism to Taipei and also the rest of the country, and will also have a negative effect on the airlines currently offering domestic flights. Plus there is a whole industry in Taipei catering to the airport. If service are moved to Taoyuan, departure and arrival slots at Taoyuan will become tighter and therefore the risk of an airprox incidents and delays will also increase.
Leaving Songshan as the commuter airport it is makes perfect sense.