There's no question that technologies like web chat and automated attendants can lower cost of service and help people get what they need quickly. All too often, however, companies buy the technology but then don't actually have the staff to provide the service. As this blog post points out.
I've used the guilty retailer of this story (Red Envelope), and I'm surprised; they're usually pretty good.
This problem could be solved really easily, too. What if the web chat started with, "Your expected wait time is 20 minutes. Would you like to leave an email for us instead?"
Of course, then they'd have to answer the email.