Unauthorized public performance is a violation of the copyright holder's exclusive rights. Market effect is only 1 of several factors examined together for a fair use defense.
It would be impractical and bad for business. They would have to hang out in parks waiting for someone to infringe. Then identify them. They would get a reputation for suing people who just wanted to listen to music in the park. And courts would be sympathetic to fair use claims in such cases.
