The module currently works out of the box, which is great. But that also comes with loads of problems once you want to change something. The way the module currently works is not very suitable for websites that, for example, have a mobile theme where they don't want to use the chat.
How about providing an option to output the chat in a block? That way it can be avoided on mobile sites, and it will also be a lot easier to control from a theming perspective.