"The mystery to me seems to be that if they are this bad, how come they apparently hold so much power?"
Basically - politics
The president, Labhras O Murchu is a State Senator
In the fifties and sixties they acted as a link between Ireland and those who had emigrated
Irish music in Britain was extremely healthy in places like London - the 1950s was the Golden Age
Comhaltas was formed to formally organise that music and they did so on a competitive basis, which tended to neutralise all the different styles
They got government support from the early days
Jim Carroll