(1) Some industries use live chat substantially more than others. Many developers will prefer it to a phone call; other workers more inclined to communicate quicker and more effectively by talking than typing.
(2) You're not really replacing 5 back-and-forth emails with the average person. You're replacing asking the prospect to either phone you back or send one email suggesting a time to call them. (If they take 5 emails before they agree to talk to you, they probably won't click on your live chat link either)
(3) Live chat actually has most of the perceived disadvantages of both email (lots of typing, uncertainty over when the other party will actually reply when initiating contact, less human interaction, permanent record of any mistakes) and telephone (immediate response expected once the conversation has started, irrespective of interruptions or whether it's a really complicated question)
I can imagine this working pretty well for selling to developers and startups and pretty badly for selling to (e.g) other salespeople, professional services, traditional middle management.