Considering the number of flagrant and willful violations of copyrights, it doesn't surprise me they would have a large legal staff; and given the number of artists, works and venues to be handled and patrolled, and the large sums involved, it doesn't surprise me that a sizeable proportion goes to administration.
The majority of what most "folk" performers play nowadays is indeed copyrighted material, so ASCAP's claims are, in the main, supportable, even if many of their contentions are of dubious validity. Ostensibly, they are not charging for ALL the music played, only the likely percentage which does fall within their rightful domain. If you can devise a better, more cost-effective, more equitable way of distributing royalties which places fewer burdens on venues or performers, please, go into business doing it and put ASCAP out of theirs.
That said, I still think it's a rip due to the sampling approach, and disproportionately unfair to small venues and artists. But then, I think the century-plus copyright periods, with durations often difficult to determine, are a bigger rip. I think it's also a rip that people can claim "arrangement" copyrights for work that is stylistically generic. Why aren't you chewing the ears off your legislators??