I've said this once, and I'll say it again. For every 100 people that want to do business exclusively online with little to no contact with a human, there are at least 10-20 people who DO want to have live contact. A lot can be lost and miscommunicated via emails, text messages, twittering, and other forms of non-human communication; therefore, nothing can take the place of a live person (via phone or in-person).
In my business, people want to know that if something goes wrong they can get a hold of someone within a relatively short period of time. Being accessible via the phone is like having insurance; nobody really realizes just how important it is to be able to reach someone via the phone, until they need to reach someone via the phone. I'm accessible to all of my clients through whatever medium they prefer. I may not be available 24/7, but I do pride myself in getting back to my clients within a relatively short time frame. With that being said, I don't mind the email only clients no more than the ones who prefer to speak directly on the phone. I believe you need to do what is best on an individual basis, and provide multiple options; versus just foisting a "once size fits all" way of doing business. Now, go back to work and answer your phone!