I would rather have a permit than a ban.
I think anybody living in an area where the parks are off limits would agree.
But, don't make it just a money grab. Create a permit process where the application needs signed off by a local metal detecting club. The applicant would demonstrate basic knowledge of metal detecting, including target discrimination and retrieval. Pass a short quiz and skills test, basically. If there are any local rules such as time of day, or particular off-limit parks or park areas like ball fields, then throw that info in, too. They need to sign something about what to do in the unlikely event they stumble across native artifacts.
The applicant leaves the metal detecting club with a FAQ sheet and approved application. The parks department take the application, a fee, and issues a permit.
Lots of other things could be done other than a heavy handed total ban. They might consider only issuing X number of permits per year, maybe limit hunting to certain hours, maybe only issue to residents, maybe rotate through the parks, maybe limit hole depth and diameter. Get busted not covering holes, digging huge holes, digging in off limit areas, and get the permit revoked for a year. Busted again and no more permits.