Personally I wouldn't want to host my sites with company that didn't have live chat support. I wouldn't want to run a hosting business either without providing such service.
Host that I'm with has live chat support and it is a very good option. You get help immediately and you don't have to wait to get a response to your support ticket.
Honestly, I can't imagine a hosting provider without that. I currently have hosting accounts with one hosting that has and the one that has not live chat support. I can tell you that difference is noticeable.
Each hosting company should have a Live Chat support as we cant prefer any hosting company who only provides support via Help Desk. Because when there is an immediate response required for some serious issues it cant be solved with the Help Desk system.
The availability of 24/7/365, live customer support is indeed critical. Users can ask questions and get speedy response. Alternatively, you can also solve technical problems at hand.
It is very essential that every web host should have a Live Chat Help Desk, but response time to customer is more important, however, sometimes time lag happens, because hosting service provider face a lot of chats or tickets in one time due to some reasons.