...to provide trolls with a place to engage in their behaviour.
You are the site operator: You get to decide what's acceptable and what isn't.
There will be some (usually the trolls themselves) who will claim you're violating their 1st amendment rights. You're not. The 1st amendment to the US Constitution has to do with *public* spaces. A web site you host or manage is like a room in your house, and you have the right to decide who comes through the front door.
So while I would first advocate the "thanks for your feedback" approach, if more restrictive measures are needed, such as mandatory registration with validation of personal details/e-mail address, paid access, or the institution of filtering to prevent the trolls from continuing, that's YOUR decision and your decision ALONE to make.
It is better to live rich than to die rich. -- Samuel Johnson