Everyone remembers ACORN, the community organizing group that engaged in voter fraud and operational irregularities (among other things). Their shadiness was brought to light in 2009 and became the subject of multiple investigations and civil lawsuits which inevitably bankrupted the organization. This was the right thing to happen.
Civil lawsuits may very well be the key to getting the looters and rioters under control in the absence of government leadership. Don’t focus on arresting the perpetrator; if someone’s property is damaged, police cars are destroyed, businesses are vandalized, these acts should result in lawsuits against the agitators. But here’s the key: if they are working for or encouraged by an organization (such as Black Lives Matter or Antifa, for example), you sue the organization as well. Of course the organization can say that they didn’t tell the rioters to do any damage, but then you have rioters who will not be held liable for their actions and being hung out to dry by their organizations, so they’ll make a deal. That’s how you put them out of business.
The agitators should be held criminally liable, but whether they are or aren’t, they should be sued. Any lawsuits, therefore, must be civil, not criminal. Maybe you can’t prove beyond a reasonable doubt in a criminal case, but you’ll have plenty of evidence for a civil suit. Once people realize that if these do these egregious actions and will be held liable and financially responsible, maybe they’ll think twice about inflicting harm on another person or property.