Nice rant but, like those popups that ask for your email when you show signs of leaving the site , the proof is in the pudding - do these live chats increase conversions?
Developers are somewhat different from the general population in that we like to read documentation rather than going to a person for help. But for almost everyone else having someone to answer a question immediately is the preferred experience.
In the parent's scenario, it seems likely that the buyer for that enterprise was simply browsing through the site, or perhaps looking at various options, when they found the parent's site, saw that there was a chat and saw the near immediate response, asked a few questions and eventually set up a meeting. To do that over email would have likely taken days.
Source: I've had something like this happen too.
Anecdotally, I've had far more success DM'ing companies on Twitter -- I don't think I've ever gotten a bot-like, automated response when taking that route, and I've had really specific questions answered quickly and thoroughly.