Why do you think there's necessarily a preemptive blanket ban being asked for? Here is the specific request for relief from the suit itself:

"REQUEST FOR RELIEF

Plaintiffs respectfully request that the Court issue judgment against Defendants as follows:

a. Declaring that Defendants’ policies and customs described in this Complaint are unlawful and violate the Fourth Amendment (incorporated through the Fourteenth Amendment) to the U.S. Constitution;

b. Permanently enjoining Defendants from operating the Flock Cameras;

c. Ordering Defendants to delete all images, records, and other data generated by the Flock Cameras;

d. Permanently enjoining Defendants and their officers, employees, agents, and any others acting on their behalf from using the Flock Cameras to collect images or information without first obtaining a warrant based on probable cause;

e. Permanently enjoining Defendants and their officers, employees, agents, and any others acting on their behalf from accessing any images, records, or other data generated by the Flock Cameras without first obtaining a warrant based on probable cause;

f. Awarding Plaintiffs’ counsel reasonable attorneys’ fees and litigation costs, including but not limited to fees, costs, and disbursements pursuant to 42 U.S.C. § 1988; and

g. Ordering all other relief to which Plaintiffs are entitled, regardless of whether such relief is demanded in this Complaint."

You could argue that point b is a blanket ban, but in fact it's kinda limited: it asks to prohibit the city from operating the cameras, but says nothing of any other party operating them. All the other points simply ask for the city to be required to obtain a warrant, just like it would have to do under normal circumstances.