My quick take on that is the majority of the traffic would move to that "private" board and the person, usually one who has paid for largely unfettered access to the site, would be left posting to themselves on an abandoned board that people won't read because they haven't figured out how to use either our software-provided filtering or their own internal filtering mechanism.
Or they'd still be getting shouted down by people who just don't want their posts existing without being "appropriately" shouted down and discredited.
Keep in mind that this is an extension of "filtering" as it was discussed some time back. That we were making it a non-premium feature on a trial basis on assurances it would completely solve the problem and with the understanding it was likely to go back to being a premium feature.
It didn't solve the problem. Obviously. It's failed so miserably that it's tough to make a case for even a limited version of it being available for free.
I'm equally convinced that not only would "private boards" cause a new set of problems, they would prove to be another example of wasted effort. They'd "solve" nothing. They'd make a lot of people happy, but the problem they'd supposedly address wouldn't be solved and we'd take on thornier problems in the process.
I'm not claiming to have the solution to the "problem". I'm not sure one exists. In fact, I'm pretty certain one doesn't.