As not very many people seem to want to be helpful, I will do my best to present what I think are the pros and cons.
Pros: I think chatbox is a valuable way to contact, see, and be up-to-date easily and quickly. It removes the issues with time lag from PM’s, and it is right in the website. It also lets you see who is on at what time. It also lets you ask a quick question right then, and have it answered.
cons: spammers abound. Many, many requests happen there, and it is ALWAYS annoying. Bad posts are common, and well, bad.
I think you can fix these issues with a new rank of moderators, like a very low level. They would be able to delete chatbox messages and report spammers. They would have to go through screening, but less vigorous. They would also not be able to report anyone with a higher non-purchased rank.
It would also be nice if you got a notification when you were quoted in the chatbox. Maybe a way to make your messages only viewable to those you quoted?
In conclusion, I think the chatbox should stay with some modifications.