The fact that you can see what your customer is typing in real time and you can start thinking about a solution for their problem.
The same thing as what I like - it's difficult not to start typing in the response but once you do, they can see that you are typing something and stop typing themselves. They won't send the message because they're waiting for your message and you can't send your message because it answers the question they won't send. And I don't think there's a way to disable automated greetings.
Don't hesitate to contact their support - they're friendly and know their stuff.
Customer success. Customers that contact us are more likely to convert and LiveChat fills the gap between rather inconvenient email and personal phone. Plus it comes with a knowledge base (we build it organically, as customers come up with questions) and a ticket system.