I suppose LiveChat is fine for receiving answers to quick questions or trivial issues in terms of the hosting account, control panel, billing or quick sales question etc. However, if the client has a complex matter which requires the technician to logon their server so they may investigate, a ticket would be the ideal approach. The last thing any company would want is their client waiting on live chat while the support tech is trying to troubleshoot/resolve the issue at hand. At the end of the day, having both parties on the line for a longer than usual duration may cause frustration on both fronts. The client may be waiting impatiently while a specific daemon may be down and the other is working frenetically to keep the client happy
I would say; LiveChat and a Ticket System serve their purpose well
Regards,