I say no.
1. You cant single out one or two people for all the drama. It's not just them, there's many people who cause drama. It'd be unfair in many ways, and those who do get muted/banned deserve it for some reason or another. Let them get it on their own time.
2. Mute them, or whatever, they could just come back on an alt. Most people have more than one account, too.
3. IMO this would just make the drama worse rather than better.