What if we only offered online customer service?

I came across this interesting thread on the UK Business Labs Forum in which a business owner was thinking about switching their online and phone service for customer service to strictly online only, eliminating the phone element. Many customers though still feel the need to physically speak to representatives on the phone right off the bat and when things aren’t being explained well online through instant messaging. Do you think this is a wise decision to remove phone service from their customer service initiatives?