There are a few add-ons available for Xenforo that provide this 'chat box' functionality. We've installed none to date. Maybe we'll add one later, perhaps for a trial run to see how it goes before deciding on a permanent Go-NoGo on it.
Main reason is moderation, and enforcement of rules. We're already struggling in some areas to get and keep decent moderators. Seems foolish to add yet another area for people to misbehave and we can't police it. Mind you, 'policing it' is not the gray line of what's considered tasteless or offensive, we still get plenty of that in TL. It's more for the BLUA and ensuring the site and members stay safe.
Bottom line - it's been considered, but admin would want to try it out for a bit before considering putting such a thing public. And quite frankly, it falls below the water line of resources when the list is prioritized. Still, it stays on the list because it IS something folks have expressed a want-need for (not just yourself).