I belong to the Calliope: the Pittsburgh Folk Music Society and serve on several of there committees including concert planning committee. We pay a fee on a per/event basis. I don't know if this because we don't own a venue and rent a hall for our concerts or why.
As far as I can tell a lot of ASCRAP's teeth is just the rollover factor. Big monster ASCRAP(not a typo) comes along and says "Feed me" and presenter's cave in the same way the bank will tack on BS fees to your statement knowing most people won't question it. We periodically make archival tapes when permitted and it's amazing how many times we find that we just paid out $100 dollars for an evening of public domain material or original material by the artists performing. And then regardless of whose material is played the artists who have the most material registered get most of the $$$. In other words, you play "Louie Louie" and the fee goes to Paul McCartney and the estate of John Lennon. Utah Phillips, when he came to perform for us called them the scourge of the music world. (We payed an ascap fee for him to play his own stuff and public domain stuff too!)
At any rate, getting eventually at hand, in our case it's the presenter's responsibility. However, we feature artists with enough bargaining clout that they can dictate policy to us to some extent. For a small unknown performer at an established club it may be different.